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    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
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    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
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    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_bxsl_InterestRateSwap7Member_label_en-US" xlink:label="lab_bxsl_InterestRateSwap7Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 7 [Member]</link:label>
    <link:label id="lab_bxsl_InterestRateSwap7Member_documentation_en-US" xlink:label="lab_bxsl_InterestRateSwap7Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 7</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InterestRateSwap7Member" xlink:href="bxsl-20260930.xsd#bxsl_InterestRateSwap7Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InterestRateSwap7Member" xlink:to="lab_bxsl_InterestRateSwap7Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019fd71c-091c-78f1-a91b-8254a79b6377_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_019fd71c-09af-73de-b58c-fdc2de130a9f_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019fd71c-09af-7e83-b0ae-b8355d949c90_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_VariableRateScenarioDomain_019fd71c-09af-73d2-bd5b-05bb7d14731a_terseLabel_en-US" xlink:label="lab_bxsl_VariableRateScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate Scenario [Domain]</link:label>
    <link:label id="lab_bxsl_VariableRateScenarioDomain_label_en-US" xlink:label="lab_bxsl_VariableRateScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate Scenario [Domain]</link:label>
    <link:label id="lab_bxsl_VariableRateScenarioDomain_documentation_en-US" xlink:label="lab_bxsl_VariableRateScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Rate Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_VariableRateScenarioDomain" xlink:href="bxsl-20260930.xsd#bxsl_VariableRateScenarioDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_VariableRateScenarioDomain" xlink:to="lab_bxsl_VariableRateScenarioDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage_019fd71c-09af-7410-a20f-29d25f49b9cf_terseLabel_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Catch-up amount prior to the waiver period</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage_label_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Catch-Up Amount, Percentage</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage_documentation_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Catch-Up Amount, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage" xlink:href="bxsl-20260930.xsd#bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage" xlink:to="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable_019fd71c-091c-7e10-a2e5-149248b35f73_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Interest and Dividends Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayableInvestmentPurchase_019fd71c-09af-7d51-973e-d8a28c25aced_terseLabel_en-US" xlink:label="lab_us-gaap_PayableInvestmentPurchase" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payable for investments</link:label>
    <link:label id="lab_us-gaap_PayableInvestmentPurchase_label_en-US" xlink:label="lab_us-gaap_PayableInvestmentPurchase" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payable, Investment, Purchase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayableInvestmentPurchase" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PayableInvestmentPurchase"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayableInvestmentPurchase" xlink:to="lab_us-gaap_PayableInvestmentPurchase" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_019fd71c-09af-7e25-b4a0-5e05c4c67515_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets Measured on Recurring Basis</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossRealized_019fd71c-09ae-7528-90f1-215ae8b972f1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossRealized" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net realized (gain) loss on foreign currency transactions</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossRealized_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossRealized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Foreign Currency Transaction, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossRealized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainLossRealized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionGainLossRealized" xlink:to="lab_us-gaap_ForeignCurrencyTransactionGainLossRealized" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_SMBCCapitalMarketsIncMember_019fd71c-09ae-74a5-8633-f0429964a917_terseLabel_en-US" xlink:label="lab_bxsl_SMBCCapitalMarketsIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SMBC Capital Markets, Inc.</link:label>
    <link:label id="lab_bxsl_SMBCCapitalMarketsIncMember_label_en-US" xlink:label="lab_bxsl_SMBCCapitalMarketsIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SMBC Capital Markets, Inc [Member]</link:label>
    <link:label id="lab_bxsl_SMBCCapitalMarketsIncMember_documentation_en-US" xlink:label="lab_bxsl_SMBCCapitalMarketsIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">SMBC Capital Markets, Inc</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_SMBCCapitalMarketsIncMember" xlink:href="bxsl-20260930.xsd#bxsl_SMBCCapitalMarketsIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_SMBCCapitalMarketsIncMember" xlink:to="lab_bxsl_SMBCCapitalMarketsIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_WirelessTelecommunicationServicesSectorMember_019fd71c-09af-787c-993b-f6477e867dec_terseLabel_en-US" xlink:label="lab_bxsl_WirelessTelecommunicationServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Wireless Telecommunication Services</link:label>
    <link:label id="lab_bxsl_WirelessTelecommunicationServicesSectorMember_label_en-US" xlink:label="lab_bxsl_WirelessTelecommunicationServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Wireless Telecommunication Services Sector [Member]</link:label>
    <link:label id="lab_bxsl_WirelessTelecommunicationServicesSectorMember_documentation_en-US" xlink:label="lab_bxsl_WirelessTelecommunicationServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Wireless Telecommunication Services Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_WirelessTelecommunicationServicesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_WirelessTelecommunicationServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_WirelessTelecommunicationServicesSectorMember" xlink:to="lab_bxsl_WirelessTelecommunicationServicesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_SaleOfStockRemainingAuthorizedAmount_019fd71c-09af-7f67-b0fe-71b5b917131e_terseLabel_en-US" xlink:label="lab_bxsl_SaleOfStockRemainingAuthorizedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining available for issuance</link:label>
    <link:label id="lab_bxsl_SaleOfStockRemainingAuthorizedAmount_label_en-US" xlink:label="lab_bxsl_SaleOfStockRemainingAuthorizedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Remaining Authorized Amount</link:label>
    <link:label id="lab_bxsl_SaleOfStockRemainingAuthorizedAmount_documentation_en-US" xlink:label="lab_bxsl_SaleOfStockRemainingAuthorizedAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale of Stock, Remaining Authorized Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_SaleOfStockRemainingAuthorizedAmount" xlink:href="bxsl-20260930.xsd#bxsl_SaleOfStockRemainingAuthorizedAmount"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_019fd71c-0a16-7e89-8fd0-43505ec5c861_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentAffiliatedIssuerNoncontrolledMember_019fd71c-09ae-71c9-8269-1e787f117f1c_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentAffiliatedIssuerNoncontrolledMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-controlled/affiliated investments</link:label>
    <link:label id="lab_us-gaap_InvestmentAffiliatedIssuerNoncontrolledMember_label_en-US" xlink:label="lab_us-gaap_InvestmentAffiliatedIssuerNoncontrolledMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Affiliated Issuer, Noncontrolled [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentAffiliatedIssuerNoncontrolledMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentAffiliatedIssuerNoncontrolledMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentAffiliatedIssuerNoncontrolledMember" xlink:to="lab_us-gaap_InvestmentAffiliatedIssuerNoncontrolledMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_April2028NotesMember_019fd71c-09af-7528-a269-dd51e242447d_terseLabel_en-US" xlink:label="lab_bxsl_April2028NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">April 2028 Notes</link:label>
    <link:label id="lab_bxsl_April2028NotesMember_label_en-US" xlink:label="lab_bxsl_April2028NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">April 2028 Notes [Member]</link:label>
    <link:label id="lab_bxsl_April2028NotesMember_documentation_en-US" xlink:label="lab_bxsl_April2028NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">April 2028 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_April2028NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_April2028NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_April2028NotesMember" xlink:to="lab_bxsl_April2028NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019fd71c-09af-7764-8feb-b545dd1a9278_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AtTheMarketOfferingOffering2Member_019fd71c-09af-7f1f-bf28-2e2a60335f4a_terseLabel_en-US" xlink:label="lab_bxsl_AtTheMarketOfferingOffering2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">At-the-Market Offering, Offering 2</link:label>
    <link:label id="lab_bxsl_AtTheMarketOfferingOffering2Member_label_en-US" xlink:label="lab_bxsl_AtTheMarketOfferingOffering2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">At-the-Market Offering, Offering 2 [Member]</link:label>
    <link:label id="lab_bxsl_AtTheMarketOfferingOffering2Member_documentation_en-US" xlink:label="lab_bxsl_AtTheMarketOfferingOffering2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">At-the-Market Offering, Offering 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AtTheMarketOfferingOffering2Member" xlink:href="bxsl-20260930.xsd#bxsl_AtTheMarketOfferingOffering2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AtTheMarketOfferingOffering2Member" xlink:to="lab_bxsl_AtTheMarketOfferingOffering2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember_019fd71c-091c-70f5-af39-06cb9142b5aa_terseLabel_en-US" xlink:label="lab_bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State Street Sub-Administration Agreement and Custody Agreement</link:label>
    <link:label id="lab_bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember_label_en-US" xlink:label="lab_bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">State Street Sub-Administration Agreement and Custody Agreement [Member]</link:label>
    <link:label id="lab_bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember_documentation_en-US" xlink:label="lab_bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sub-Administration Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember" xlink:href="bxsl-20260930.xsd#bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember" xlink:to="lab_bxsl_StateStreetSubAdministrationAgreementAndCustodyAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A3625NotesDue2026Member_019fd71c-091c-7326-ab40-2c0049a5304d_terseLabel_en-US" xlink:label="lab_bxsl_A3625NotesDue2026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3.625% Notes Due 2026</link:label>
    <link:label id="lab_bxsl_A3625NotesDue2026Member_label_en-US" xlink:label="lab_bxsl_A3625NotesDue2026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">3.625% Notes Due 2026 [Member]</link:label>
    <link:label id="lab_bxsl_A3625NotesDue2026Member_documentation_en-US" xlink:label="lab_bxsl_A3625NotesDue2026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">3.625% Notes Due 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A3625NotesDue2026Member" xlink:href="bxsl-20260930.xsd#bxsl_A3625NotesDue2026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A3625NotesDue2026Member" xlink:to="lab_bxsl_A3625NotesDue2026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableCapitalGainBased_019fd71c-09af-71c3-b3ee-0bd3f834596d_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableCapitalGainBased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital gains based incentive fees payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableCapitalGainBased_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableCapitalGainBased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Incentive Fee Payable, Capital-Gain-Based</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInIncentiveFeePayableCapitalGainBased" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInIncentiveFeePayableCapitalGainBased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInIncentiveFeePayableCapitalGainBased" xlink:to="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableCapitalGainBased" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InterestRateSwap2Member_019fd71c-09af-7510-b502-a603dff09f5b_terseLabel_en-US" xlink:label="lab_bxsl_InterestRateSwap2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 2</link:label>
    <link:label id="lab_bxsl_InterestRateSwap2Member_label_en-US" xlink:label="lab_bxsl_InterestRateSwap2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 2 [Member]</link:label>
    <link:label id="lab_bxsl_InterestRateSwap2Member_documentation_en-US" xlink:label="lab_bxsl_InterestRateSwap2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InterestRateSwap2Member" xlink:href="bxsl-20260930.xsd#bxsl_InterestRateSwap2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InterestRateSwap2Member" xlink:to="lab_bxsl_InterestRateSwap2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FeeIncome_019fd71c-09af-71af-b290-6c7be61c98b9_terseLabel_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_us-gaap_FeeIncome_label_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FeeIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FeeIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FeeIncome" xlink:to="lab_us-gaap_FeeIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AirFreightLogisticsSectorMember_019fd71c-09ae-7c4a-9dbc-85aa8fe24a87_terseLabel_en-US" xlink:label="lab_bxsl_AirFreightLogisticsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Air Freight &amp; Logistics</link:label>
    <link:label id="lab_bxsl_AirFreightLogisticsSectorMember_label_en-US" xlink:label="lab_bxsl_AirFreightLogisticsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Air Freight &amp; Logistics Sector [Member]</link:label>
    <link:label id="lab_bxsl_AirFreightLogisticsSectorMember_documentation_en-US" xlink:label="lab_bxsl_AirFreightLogisticsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Air Freight &amp; Logistics Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AirFreightLogisticsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_AirFreightLogisticsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AirFreightLogisticsSectorMember" xlink:to="lab_bxsl_AirFreightLogisticsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019fd71c-09af-7ef8-8dbd-b7d664108999_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agreements and Related Party Transactions</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_NewACIIntermediateILLCSecondLienDebtMember_019fd71c-0a16-73f1-b4bd-edbe982620c9_terseLabel_en-US" xlink:label="lab_bxsl_NewACIIntermediateILLCSecondLienDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New ACI Intermediate I, LLC - Second Lien Debt</link:label>
    <link:label id="lab_bxsl_NewACIIntermediateILLCSecondLienDebtMember_label_en-US" xlink:label="lab_bxsl_NewACIIntermediateILLCSecondLienDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New ACI Intermediate I, LLC - Second Lien Debt [Member]</link:label>
    <link:label id="lab_bxsl_NewACIIntermediateILLCSecondLienDebtMember_documentation_en-US" xlink:label="lab_bxsl_NewACIIntermediateILLCSecondLienDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New ACI Intermediate I, LLC - Second Lien Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_NewACIIntermediateILLCSecondLienDebtMember" xlink:href="bxsl-20260930.xsd#bxsl_NewACIIntermediateILLCSecondLienDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_NewACIIntermediateILLCSecondLienDebtMember" xlink:to="lab_bxsl_NewACIIntermediateILLCSecondLienDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_CommercialServicesSuppliesSectorMember_019fd71c-09af-78c8-8534-7259b762cb6a_terseLabel_en-US" xlink:label="lab_bxsl_CommercialServicesSuppliesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Services &amp; Supplies</link:label>
    <link:label id="lab_bxsl_CommercialServicesSuppliesSectorMember_label_en-US" xlink:label="lab_bxsl_CommercialServicesSuppliesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Services &amp; Supplies Sector [Member]</link:label>
    <link:label id="lab_bxsl_CommercialServicesSuppliesSectorMember_documentation_en-US" xlink:label="lab_bxsl_CommercialServicesSuppliesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Services &amp; Supplies Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_CommercialServicesSuppliesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_CommercialServicesSuppliesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_CommercialServicesSuppliesSectorMember" xlink:to="lab_bxsl_CommercialServicesSuppliesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements_019fd71c-09ae-7f89-9d3d-6fd2a10716ec_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ratio of net expenses to average net assets</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements_label_en-US" xlink:label="lab_bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Expense Ratio Including Fee Waiver And Reimbursements</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements_documentation_en-US" xlink:label="lab_bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Expense Ratio Including Fee Waiver And Reimbursements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements" xlink:to="lab_bxsl_InvestmentCompanyExpenseRatioIncludingFeeWaiverAndReimbursements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019fd71c-09af-7fbf-8bba-084beaa87376_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in usd per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee_019fd71c-0a16-7542-8b54-55d438dabc41_terseLabel_en-US" xlink:label="lab_bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unused commitment fees</link:label>
    <link:label id="lab_bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee_label_en-US" xlink:label="lab_bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Debt Instrument Unused Borrowing Capacity Fee</link:label>
    <link:label id="lab_bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee_documentation_en-US" xlink:label="lab_bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Payable, Debt Instrument Unused Borrowing Capacity Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee" xlink:href="bxsl-20260930.xsd#bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee" xlink:to="lab_bxsl_InterestPayableDebtInstrumentUnusedBorrowingCapacityFee" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_019fd71c-09ae-73a6-99b7-ece5b82afbc5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net accretion of discount and amortization of premium</link:label>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_label_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:to="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableIncomeBased_019fd71c-09ae-7a24-ab20-4444504f97dd_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableIncomeBased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income based incentive fees payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableIncomeBased_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableIncomeBased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Incentive Fee Payable, Income-Based</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInIncentiveFeePayableIncomeBased" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInIncentiveFeePayableIncomeBased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInIncentiveFeePayableIncomeBased" xlink:to="lab_us-gaap_IncreaseDecreaseInIncentiveFeePayableIncomeBased" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ValuationYieldAnalysisApproachMember_019fd71c-09ae-7e06-a2d4-2a216f9c9e63_terseLabel_en-US" xlink:label="lab_bxsl_ValuationYieldAnalysisApproachMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Yield Analysis</link:label>
    <link:label id="lab_bxsl_ValuationYieldAnalysisApproachMember_label_en-US" xlink:label="lab_bxsl_ValuationYieldAnalysisApproachMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation, Yield Analysis Approach [Member]</link:label>
    <link:label id="lab_bxsl_ValuationYieldAnalysisApproachMember_documentation_en-US" xlink:label="lab_bxsl_ValuationYieldAnalysisApproachMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation, Yield Analysis Approach</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ValuationYieldAnalysisApproachMember" xlink:href="bxsl-20260930.xsd#bxsl_ValuationYieldAnalysisApproachMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ValuationYieldAnalysisApproachMember" xlink:to="lab_bxsl_ValuationYieldAnalysisApproachMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_019fd71c-09af-7c75-a90a-78150a9b6489_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019fd71c-09af-7f4f-87b2-a14db6a34243_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss_019fd71c-091c-755e-8513-b94dce311cac_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net change due to hedging activity</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Fair Value Hedge, Included in Effectiveness, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss" xlink:to="lab_us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A5.900NotesDue2031Member_019fd71c-0a16-7d93-9bd9-c2387c308bfb_terseLabel_en-US" xlink:label="lab_bxsl_A5.900NotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.900% Notes Due 2031</link:label>
    <link:label id="lab_bxsl_A5.900NotesDue2031Member_label_en-US" xlink:label="lab_bxsl_A5.900NotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5.900% Notes Due 2031 [Member]</link:label>
    <link:label id="lab_bxsl_A5.900NotesDue2031Member_documentation_en-US" xlink:label="lab_bxsl_A5.900NotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5.900% Notes Due 2031</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A5.900NotesDue2031Member" xlink:href="bxsl-20260930.xsd#bxsl_A5.900NotesDue2031Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A5.900NotesDue2031Member" xlink:to="lab_bxsl_A5.900NotesDue2031Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_BuildingProductsSectorMember_019fd71c-091c-71e2-a038-dc488c753155_terseLabel_en-US" xlink:label="lab_bxsl_BuildingProductsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building Products</link:label>
    <link:label id="lab_bxsl_BuildingProductsSectorMember_label_en-US" xlink:label="lab_bxsl_BuildingProductsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building Products Sector [Member]</link:label>
    <link:label id="lab_bxsl_BuildingProductsSectorMember_documentation_en-US" xlink:label="lab_bxsl_BuildingProductsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Building Products Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_BuildingProductsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_BuildingProductsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_BuildingProductsSectorMember" xlink:to="lab_bxsl_BuildingProductsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019fd71c-09ae-7234-884d-89cdb6ae1709_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare_019fd71c-09af-7549-a880-0ee218c2b37a_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income, basic (in usd per share)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Investment Income (Loss), Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" xlink:to="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentInterestRate_019fd71c-09af-752f-b2cd-aae8cc56bfef_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_us-gaap_InvestmentInterestRate_label_en-US" xlink:label="lab_us-gaap_InvestmentInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentInterestRate" xlink:to="lab_us-gaap_InvestmentInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentInterestRateFloor_019fd71c-09af-7214-933a-16bc587b8b78_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentInterestRateFloor" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate, floor</link:label>
    <link:label id="lab_us-gaap_InvestmentInterestRateFloor_label_en-US" xlink:label="lab_us-gaap_InvestmentInterestRateFloor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Interest Rate, Floor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentInterestRateFloor" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentInterestRateFloor"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentInterestRateFloor" xlink:to="lab_us-gaap_InvestmentInterestRateFloor" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A20241NotesMember_019fd71c-09af-7cd5-80fc-9d4fd7a48bf3_terseLabel_en-US" xlink:label="lab_bxsl_A20241NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024-1 Notes</link:label>
    <link:label id="lab_bxsl_A20241NotesMember_label_en-US" xlink:label="lab_bxsl_A20241NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024-1 Notes [Member]</link:label>
    <link:label id="lab_bxsl_A20241NotesMember_documentation_en-US" xlink:label="lab_bxsl_A20241NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024-1 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A20241NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_A20241NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A20241NotesMember" xlink:to="lab_bxsl_A20241NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_country_US_019fd71c-09af-7acf-b0d6-5080c0b5d0d0_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">United States</link:label>
    <link:label id="lab_country_US_label_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_US" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_US"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_US" xlink:to="lab_country_US" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesScenarioDomain_019fd71c-09ae-7f40-bbdf-dda0b604b249_terseLabel_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Scenario [Domain]</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesScenarioDomain_label_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Scenario [Domain]</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesScenarioDomain_documentation_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_IncomeBasedIncentiveFeesScenarioDomain" xlink:href="bxsl-20260930.xsd#bxsl_IncomeBasedIncentiveFeesScenarioDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_IncomeBasedIncentiveFeesScenarioDomain" xlink:to="lab_bxsl_IncomeBasedIncentiveFeesScenarioDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsDomain_01a198ab-4d87-7621-b728-ddeafac8399e_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends [Domain]</link:label>
    <link:label id="lab_us-gaap_DividendsDomain_label_en-US" xlink:label="lab_us-gaap_DividendsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsDomain" xlink:to="lab_us-gaap_DividendsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendIncomeOperating_019fd71c-09ae-75c7-bf98-18dda3cf37a0_terseLabel_en-US" xlink:label="lab_us-gaap_DividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend income</link:label>
    <link:label id="lab_us-gaap_DividendIncomeOperating_label_en-US" xlink:label="lab_us-gaap_DividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendIncomeOperating" xlink:to="lab_us-gaap_DividendIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_019fd71c-09af-7358-b4a7-eb219908e986_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019fd71c-0a16-7b10-82dd-c7d88c7a3781_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_HealthCareTechnologySectorMember_019fd71c-09af-7762-9a01-fff5815da787_terseLabel_en-US" xlink:label="lab_bxsl_HealthCareTechnologySectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Health Care Technology</link:label>
    <link:label id="lab_bxsl_HealthCareTechnologySectorMember_label_en-US" xlink:label="lab_bxsl_HealthCareTechnologySectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Health Care Technology Sector [Member]</link:label>
    <link:label id="lab_bxsl_HealthCareTechnologySectorMember_documentation_en-US" xlink:label="lab_bxsl_HealthCareTechnologySectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Health Care Technology Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_HealthCareTechnologySectorMember" xlink:href="bxsl-20260930.xsd#bxsl_HealthCareTechnologySectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_HealthCareTechnologySectorMember" xlink:to="lab_bxsl_HealthCareTechnologySectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019fd71c-09af-7a7f-adbe-4d69bd65a3df_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities_019fd71c-0a16-7608-9c9a-2d617c767aec_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral Received</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Security Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralObligationToReturnSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:to="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfTreasuryStockTable_019fd71c-09ae-7bbb-8597-1703423057e5_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfTreasuryStockTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Treasury Stock [Table]</link:label>
    <link:label id="lab_us-gaap_ClassOfTreasuryStockTable_label_en-US" xlink:label="lab_us-gaap_ClassOfTreasuryStockTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Treasury Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfTreasuryStockTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfTreasuryStockTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfTreasuryStockTable" xlink:to="lab_us-gaap_ClassOfTreasuryStockTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_019fd71c-091c-7a24-82c8-4f1a1ec00ca6_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019fd71c-09af-746d-8176-9c5e801cac62_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_NewACIBuyerLLCFirstLienDebt1Member_019fd71c-0a16-7ed3-bea1-3a0268be6495_terseLabel_en-US" xlink:label="lab_bxsl_NewACIBuyerLLCFirstLienDebt1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New ACI Buyer, LLC - First Lien Debt</link:label>
    <link:label id="lab_bxsl_NewACIBuyerLLCFirstLienDebt1Member_label_en-US" xlink:label="lab_bxsl_NewACIBuyerLLCFirstLienDebt1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New ACI Buyer, LLC - First Lien Debt 1 [Member]</link:label>
    <link:label id="lab_bxsl_NewACIBuyerLLCFirstLienDebt1Member_documentation_en-US" xlink:label="lab_bxsl_NewACIBuyerLLCFirstLienDebt1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New ACI Buyer, LLC - First Lien Debt 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_NewACIBuyerLLCFirstLienDebt1Member" xlink:href="bxsl-20260930.xsd#bxsl_NewACIBuyerLLCFirstLienDebt1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_NewACIBuyerLLCFirstLienDebt1Member" xlink:to="lab_bxsl_NewACIBuyerLLCFirstLienDebt1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_019fd71c-09ae-7271-9a30-59f21ce75e41_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn_019fd71c-09af-710b-8cc6-df99732cfe03_terseLabel_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pre incentive fee cap percentage</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn_label_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Cap, Percentage Of Cumulative Net Return</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn_documentation_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Cap, Percentage Of Cumulative Net Return</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn" xlink:href="bxsl-20260930.xsd#bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn" xlink:to="lab_bxsl_IncomeBasedIncentiveFeesCapPercentageOfCumulativeNetReturn" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019fd71c-09af-7fb4-91a8-6509809cf4c8_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Aggregate principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019fd71c-09af-7c57-a895-82f17a76348a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Principal Committed</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ValuationMarketQuotationsMember_019fd71c-09af-752e-ba4d-f10d5c4b5dad_terseLabel_en-US" xlink:label="lab_bxsl_ValuationMarketQuotationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Market Quotations</link:label>
    <link:label id="lab_bxsl_ValuationMarketQuotationsMember_label_en-US" xlink:label="lab_bxsl_ValuationMarketQuotationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation, Market Quotations [Member]</link:label>
    <link:label id="lab_bxsl_ValuationMarketQuotationsMember_documentation_en-US" xlink:label="lab_bxsl_ValuationMarketQuotationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation, Market Quotations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ValuationMarketQuotationsMember" xlink:href="bxsl-20260930.xsd#bxsl_ValuationMarketQuotationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ValuationMarketQuotationsMember" xlink:to="lab_bxsl_ValuationMarketQuotationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_CapitalMarketsSectorMember_019fd71c-09ae-75c9-98de-a6d598d9fc0d_terseLabel_en-US" xlink:label="lab_bxsl_CapitalMarketsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital Markets</link:label>
    <link:label id="lab_bxsl_CapitalMarketsSectorMember_label_en-US" xlink:label="lab_bxsl_CapitalMarketsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Markets Sector [Member]</link:label>
    <link:label id="lab_bxsl_CapitalMarketsSectorMember_documentation_en-US" xlink:label="lab_bxsl_CapitalMarketsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital Markets Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_CapitalMarketsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_CapitalMarketsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_CapitalMarketsSectorMember" xlink:to="lab_bxsl_CapitalMarketsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_BigSkyFundingFacilityMember_019fd71c-09ae-7866-b5ab-5e16f12582cb_terseLabel_en-US" xlink:label="lab_bxsl_BigSkyFundingFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Big Sky Funding Facility</link:label>
    <link:label id="lab_bxsl_BigSkyFundingFacilityMember_label_en-US" xlink:label="lab_bxsl_BigSkyFundingFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Big Sky Funding Facility [Member]</link:label>
    <link:label id="lab_bxsl_BigSkyFundingFacilityMember_documentation_en-US" xlink:label="lab_bxsl_BigSkyFundingFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Big Sky Funding Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_BigSkyFundingFacilityMember" xlink:href="bxsl-20260930.xsd#bxsl_BigSkyFundingFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_BigSkyFundingFacilityMember" xlink:to="lab_bxsl_BigSkyFundingFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019fd71c-09af-7d87-9672-8c05f3ee67e3_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_SoftwareSectorMember_019fd71c-09ae-736b-acd2-42e3921e742b_terseLabel_en-US" xlink:label="lab_bxsl_SoftwareSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Software</link:label>
    <link:label id="lab_bxsl_SoftwareSectorMember_label_en-US" xlink:label="lab_bxsl_SoftwareSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software Sector [Member]</link:label>
    <link:label id="lab_bxsl_SoftwareSectorMember_documentation_en-US" xlink:label="lab_bxsl_SoftwareSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Software Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_SoftwareSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_SoftwareSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_SoftwareSectorMember" xlink:to="lab_bxsl_SoftwareSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock_019fd71c-09af-728a-835c-41742fc90344_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments</link:label>
    <link:label id="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Holdings, Schedule of Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:to="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTableTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInReceivableForInvestmentSold_019fd71c-09af-79d0-ad56-5cada2b4763a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInReceivableForInvestmentSold" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Receivable for investments</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInReceivableForInvestmentSold_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInReceivableForInvestmentSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Receivable for Investment Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInReceivableForInvestmentSold" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInReceivableForInvestmentSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInReceivableForInvestmentSold" xlink:to="lab_us-gaap_IncreaseDecreaseInReceivableForInvestmentSold" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019fd71c-091c-7266-81bd-b075ada6ea40_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncentiveFeePayableCapitalGainBased_019fd71c-0a16-7a34-a919-59199abfb38c_terseLabel_en-US" xlink:label="lab_us-gaap_IncentiveFeePayableCapitalGainBased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital gains based incentive fees payable (Note 3)</link:label>
    <link:label id="lab_us-gaap_IncentiveFeePayableCapitalGainBased_label_en-US" xlink:label="lab_us-gaap_IncentiveFeePayableCapitalGainBased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incentive Fee Payable, Capital-Gain-Based</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncentiveFeePayableCapitalGainBased" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncentiveFeePayableCapitalGainBased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncentiveFeePayableCapitalGainBased" xlink:to="lab_us-gaap_IncentiveFeePayableCapitalGainBased" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_019fd71c-09ae-782f-8175-079b7d693d0f_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_019fd71c-09ae-7096-8c09-4a6fef77a545_terseLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019fd71c-09af-7833-a031-89dee4203cda_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue_019fd71c-09af-7960-9d74-02c7d9aeb07f_terseLabel_en-US" xlink:label="lab_bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate sales price</link:label>
    <link:label id="lab_bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue_label_en-US" xlink:label="lab_bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction, Value</link:label>
    <link:label id="lab_bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue_documentation_en-US" xlink:label="lab_bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue" xlink:href="bxsl-20260930.xsd#bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue" xlink:to="lab_bxsl_SaleOfStockNumberOfSharesIssuedInTransactionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_019fd71c-09af-7837-b0ef-99619cd5536e_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount Rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:to="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax_019fd71c-0a16-7d0a-a4e9-40f794698b6a_totalLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net change in unrealized appreciation (depreciation), net of income tax (provision) benefit</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax_019fd71c-0a16-7d91-befc-366c8388a4cf_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net change in unrealized appreciation (depreciation), net of income tax (provision) benefit</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss), Investment, Derivative, and Foreign Currency Transaction Price Change, Operating, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:to="lab_us-gaap_UnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchaseProgramPeriodInForce1_019fd71c-09ae-78b9-a9c9-cb2a6ea2f5f8_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramPeriodInForce1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period in force</link:label>
    <link:label id="lab_us-gaap_StockRepurchaseProgramPeriodInForce1_label_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramPeriodInForce1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Period in Force</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchaseProgramPeriodInForce1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchaseProgramPeriodInForce1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchaseProgramPeriodInForce1" xlink:to="lab_us-gaap_StockRepurchaseProgramPeriodInForce1" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember_019fd71c-091c-7d16-9b3b-0efc96894d6f_terseLabel_en-US" xlink:label="lab_bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pre-Incentive Fee Net Investment Income For Trailing Twelve Quarters Greater Than Catch-Up Amount</link:label>
    <link:label id="lab_bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember_label_en-US" xlink:label="lab_bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pre-Incentive Fee Net Investment Income For Trailing Twelve Quarters Greater Than Catch-Up Amount [Member]</link:label>
    <link:label id="lab_bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember_documentation_en-US" xlink:label="lab_bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Pre-Incentive Fee Net Investment Income For Trailing Twelve Quarters Greater Than Catch-Up Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember" xlink:href="bxsl-20260930.xsd#bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember" xlink:to="lab_bxsl_PreIncentiveFeeNetInvestmentIncomeForTrailingTwelveQuartersGreaterThanCatchUpAmountMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
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    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_019fd71c-0a16-75cc-9316-1d2153c9e81b_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentTypeConcentrationRiskMember_019fd71c-0a16-7335-b904-34151eec0aea_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentTypeConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Type Concentration Risk</link:label>
    <link:label id="lab_bxsl_InvestmentTypeConcentrationRiskMember_label_en-US" xlink:label="lab_bxsl_InvestmentTypeConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Type Concentration Risk [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentTypeConcentrationRiskMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentTypeConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Type Concentration Risk</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentTypeConcentrationRiskMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentTypeConcentrationRiskMember"/>
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    <link:label id="lab_us-gaap_DerivativeFixedInterestRate_019fd71c-091c-7ac1-9c60-6b4c40157ee3_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Receives</link:label>
    <link:label id="lab_us-gaap_DerivativeFixedInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Fixed Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFixedInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFixedInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFixedInterestRate" xlink:to="lab_us-gaap_DerivativeFixedInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_NewACIHoldingsLLCEquityAndOtherClassACommonUnitsMember_01a186f1-2ded-7e8e-80ee-c0446f1baa5a_terseLabel_en-US" xlink:label="lab_bxsl_NewACIHoldingsLLCEquityAndOtherClassACommonUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New ACI Holdings, LLC - Equity and other - Class A Common Units</link:label>
    <link:label id="lab_bxsl_NewACIHoldingsLLCEquityAndOtherClassACommonUnitsMember_label_en-US" xlink:label="lab_bxsl_NewACIHoldingsLLCEquityAndOtherClassACommonUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New ACI Holdings, LLC - Equity and other - Class A Common Units [Member]</link:label>
    <link:label id="lab_bxsl_NewACIHoldingsLLCEquityAndOtherClassACommonUnitsMember_documentation_en-US" xlink:label="lab_bxsl_NewACIHoldingsLLCEquityAndOtherClassACommonUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New ACI Holdings, LLC - Equity and other - Class A Common Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_NewACIHoldingsLLCEquityAndOtherClassACommonUnitsMember" xlink:href="bxsl-20260930.xsd#bxsl_NewACIHoldingsLLCEquityAndOtherClassACommonUnitsMember"/>
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    <link:label id="lab_us-gaap_CreditFacilityDomain_019fd71c-09ae-7203-b467-a48d81ffdd28_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtSecuritiesSecondLienMember_019fd71c-09ae-72cb-ae42-e4a7c2cddb0e_terseLabel_en-US" xlink:label="lab_bxsl_DebtSecuritiesSecondLienMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Second lien debt</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesSecondLienMember_label_en-US" xlink:label="lab_bxsl_DebtSecuritiesSecondLienMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Second Lien [Member]</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesSecondLienMember_documentation_en-US" xlink:label="lab_bxsl_DebtSecuritiesSecondLienMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Second Lien</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtSecuritiesSecondLienMember" xlink:href="bxsl-20260930.xsd#bxsl_DebtSecuritiesSecondLienMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtSecuritiesSecondLienMember" xlink:to="lab_bxsl_DebtSecuritiesSecondLienMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019fd71c-09ae-7e82-ac67-85226a238540_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember_019fd71c-09ae-749d-ada8-6295f31575c6_terseLabel_en-US" xlink:label="lab_bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Jackson Hole Funding Facility, Foreign Currency Advances</link:label>
    <link:label id="lab_bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember_label_en-US" xlink:label="lab_bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Jackson Hole Funding Facility, Foreign Currency Advances [Member]</link:label>
    <link:label id="lab_bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember_documentation_en-US" xlink:label="lab_bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Jackson Hole Funding Facility, Foreign Currency Advances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember" xlink:href="bxsl-20260930.xsd#bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember" xlink:to="lab_bxsl_JacksonHoleFundingFacilityForeignCurrencyAdvancesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock_019fd71c-091c-74b8-a203-5054edc57bc4_terseLabel_en-US" xlink:label="lab_bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Amounts Received and Shares Issued To Shareholders</link:label>
    <link:label id="lab_bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock_label_en-US" xlink:label="lab_bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Dividend Reinvestment Plan [Table Text Block]</link:label>
    <link:label id="lab_bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock_documentation_en-US" xlink:label="lab_bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Dividend Reinvestment Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock" xlink:href="bxsl-20260930.xsd#bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock" xlink:to="lab_bxsl_ScheduleOfDividendReinvestmentPlanTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3_019fd71c-091c-790c-ae24-297b5fd19664_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfers out of level 3</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3"/>
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    <link:label id="lab_us-gaap_DividendAndInterestReceivable_019fd71c-09af-7040-ad50-d09ffb77294d_terseLabel_en-US" xlink:label="lab_us-gaap_DividendAndInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest receivable from non-controlled/non-affiliated investments</link:label>
    <link:label id="lab_us-gaap_DividendAndInterestReceivable_label_en-US" xlink:label="lab_us-gaap_DividendAndInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend and Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendAndInterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendAndInterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendAndInterestReceivable" xlink:to="lab_us-gaap_DividendAndInterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019fd71c-09ae-737c-86b2-4c654d6ea22a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Fair Value of Investments Measured Using Level 3 Inputs</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherGeneralAndAdministrativeExpense_019fd71c-09ae-7935-87b5-706f42c64e14_terseLabel_en-US" xlink:label="lab_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other general and administrative expenses</link:label>
    <link:label id="lab_us-gaap_OtherGeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherGeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtSecuritiesSecondLienRealizedGainLossMember_019fd71c-091c-75f1-b455-c4ba95805447_terseLabel_en-US" xlink:label="lab_bxsl_DebtSecuritiesSecondLienRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Second Lien, Realized Gain (Loss)</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesSecondLienRealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_DebtSecuritiesSecondLienRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Second Lien, Realized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesSecondLienRealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_DebtSecuritiesSecondLienRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Second Lien, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtSecuritiesSecondLienRealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_DebtSecuritiesSecondLienRealizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtSecuritiesSecondLienRealizedGainLossMember" xlink:to="lab_bxsl_DebtSecuritiesSecondLienRealizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_019fd71c-09ae-7948-bbdd-802e675f5d9a_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Equivalents and Restricted Cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:to="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyFinancialHighlightsRollForward_019fd71c-09ae-7213-a9e2-e0c6d34be8e4_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Highlights [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyFinancialHighlightsRollForward_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Highlights [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyFinancialHighlightsRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:to="lab_us-gaap_InvestmentCompanyFinancialHighlightsRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_TransportationInfrastructureSectorMember_019fd71c-0a16-790e-8e1f-880cf4a7a69c_terseLabel_en-US" xlink:label="lab_bxsl_TransportationInfrastructureSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transportation Infrastructure</link:label>
    <link:label id="lab_bxsl_TransportationInfrastructureSectorMember_label_en-US" xlink:label="lab_bxsl_TransportationInfrastructureSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transportation Infrastructure Sector [Member]</link:label>
    <link:label id="lab_bxsl_TransportationInfrastructureSectorMember_documentation_en-US" xlink:label="lab_bxsl_TransportationInfrastructureSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transportation Infrastructure Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_TransportationInfrastructureSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_TransportationInfrastructureSectorMember"/>
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    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_RestrictedSecuritiesMember_019fd71c-09af-780d-93cb-a2de619b1f7e_terseLabel_en-US" xlink:label="lab_bxsl_RestrictedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Securities</link:label>
    <link:label id="lab_bxsl_RestrictedSecuritiesMember_label_en-US" xlink:label="lab_bxsl_RestrictedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Securities [Member]</link:label>
    <link:label id="lab_bxsl_RestrictedSecuritiesMember_documentation_en-US" xlink:label="lab_bxsl_RestrictedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_RestrictedSecuritiesMember" xlink:href="bxsl-20260930.xsd#bxsl_RestrictedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_RestrictedSecuritiesMember" xlink:to="lab_bxsl_RestrictedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive_019fd71c-09ae-7bef-b7fc-09878de7bdab_terseLabel_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Greater than 5 Years</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive_label_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term Maturities, Repayments of Principal in Rolling Year After Five</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive_documentation_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term Maturities, Repayments of Principal in Rolling Year After Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive" xlink:href="bxsl-20260930.xsd#bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive" xlink:to="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearAfterFive" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1"/>
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    <link:label id="lab_us-gaap_LongTermDebtFairValue_label_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtFairValue" xlink:to="lab_us-gaap_LongTermDebtFairValue" xlink:type="arc" order="1"/>
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    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassBPreferredUnitsMember_label_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassBPreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class B Preferred Units [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassBPreferredUnitsMember_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassBPreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class B Preferred Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassBPreferredUnitsMember" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassBPreferredUnitsMember"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_019fd71c-091c-7baf-bb1d-7a1d8a7ce04c_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:to="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:type="arc" order="1"/>
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    <link:label id="lab_bxsl_InvestmentsRealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_InvestmentsRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Realized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentsRealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentsRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentsRealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentsRealizedGainLossMember"/>
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    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1_019fd71c-0a16-7885-8583-51a916bf8220_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaps</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1"/>
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    <link:label id="lab_bxsl_DebtSecuritiesFixedRateMember_019fd71c-09ae-79cb-b237-82bb26a4865c_terseLabel_en-US" xlink:label="lab_bxsl_DebtSecuritiesFixedRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Fixed Rate</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesFixedRateMember_label_en-US" xlink:label="lab_bxsl_DebtSecuritiesFixedRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Fixed Rate [Member]</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesFixedRateMember_documentation_en-US" xlink:label="lab_bxsl_DebtSecuritiesFixedRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Fixed Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtSecuritiesFixedRateMember" xlink:href="bxsl-20260930.xsd#bxsl_DebtSecuritiesFixedRateMember"/>
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    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrExpirationDate"/>
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    <link:label id="lab_us-gaap_SubordinatedDebtMember_label_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubordinatedDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubordinatedDebtMember" xlink:to="lab_us-gaap_SubordinatedDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_AffiliatedEntityMember_019fd71c-09af-7d5d-8ad0-b88d03ddba3a_terseLabel_en-US" xlink:label="lab_srt_AffiliatedEntityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Affiliated Entity</link:label>
    <link:label id="lab_srt_AffiliatedEntityMember_label_en-US" xlink:label="lab_srt_AffiliatedEntityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Affiliated Entity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AffiliatedEntityMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_AffiliatedEntityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_AffiliatedEntityMember" xlink:to="lab_srt_AffiliatedEntityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsumerSectorMember_019fd71c-09af-7bf9-a2e0-0690173fd10e_terseLabel_en-US" xlink:label="lab_us-gaap_ConsumerSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diversified Consumer Services</link:label>
    <link:label id="lab_us-gaap_ConsumerSectorMember_label_en-US" xlink:label="lab_us-gaap_ConsumerSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consumer Sector [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsumerSectorMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsumerSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsumerSectorMember" xlink:to="lab_us-gaap_ConsumerSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_019fd71c-09ae-7486-add0-55d6ab68d382_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of Common Shares, net of offering and underwriting costs</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_019fd71c-09ae-7746-8efd-10d10ce004e2_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax_019fd71c-0a16-768f-b2ac-2361aaaab846_totalLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net investment income after tax expense</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax_019fd71c-0a16-7739-951c-d311093458ae_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income after tax expense</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Operating, after Expense and Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax" xlink:to="lab_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract_019fd71c-0a16-7771-9352-42e4b3eb91c7_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net change in unrealized appreciation (depreciation):</link:label>
    <link:label id="lab_bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract_label_en-US" xlink:label="lab_bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Recognized Unrealized Appreciation (Depreciation), Net [Abstract]</link:label>
    <link:label id="lab_bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract_documentation_en-US" xlink:label="lab_bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Owned, Recognized Unrealized Appreciation (Depreciation), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract" xlink:to="lab_bxsl_InvestmentOwnedRecognizedUnrealizedAppreciationDepreciationNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_019fd71c-091c-7583-bb55-c9c296d5338c_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTaxAbstract_019fd71c-0a16-79b6-8aee-921f0d3d1888_terseLabel_en-US" xlink:label="lab_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized gain (loss):</link:label>
    <link:label id="lab_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTaxAbstract_label_en-US" xlink:label="lab_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss), Investment and Derivative, Operating, and Foreign Currency Transaction, after Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTaxAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTaxAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTaxAbstract" xlink:to="lab_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTaxAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A2027NotesMember_019fd71c-0a16-73eb-8b8c-7acf05a45dd8_terseLabel_en-US" xlink:label="lab_bxsl_A2027NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027 Notes</link:label>
    <link:label id="lab_bxsl_A2027NotesMember_label_en-US" xlink:label="lab_bxsl_A2027NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2027 Notes [Member]</link:label>
    <link:label id="lab_bxsl_A2027NotesMember_documentation_en-US" xlink:label="lab_bxsl_A2027NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2027 Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A2027NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_A2027NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A2027NotesMember" xlink:to="lab_bxsl_A2027NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_019fd71c-09af-7734-b21a-5ce251bb4e05_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetsAbstract" xlink:to="lab_us-gaap_DerivativeAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateSwapMember_019fd71c-09af-768a-a1c4-cac84e3114a7_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap</link:label>
    <link:label id="lab_us-gaap_InterestRateSwapMember_label_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestRateSwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateSwapMember" xlink:to="lab_us-gaap_InterestRateSwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019fd71c-0a16-7297-8372-4b5556e572d9_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019fd71c-09ae-76af-b213-149be7f58d4c_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net of unamortized debt issuance costs</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OpenForwardForeignCurrencyContractIdentifierAxis_019fd71c-0a16-7cc9-a356-79710b8e7ac5_terseLabel_en-US" xlink:label="lab_us-gaap_OpenForwardForeignCurrencyContractIdentifierAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Open Forward Foreign Currency Contract, Identifier [Axis]</link:label>
    <link:label id="lab_us-gaap_OpenForwardForeignCurrencyContractIdentifierAxis_label_en-US" xlink:label="lab_us-gaap_OpenForwardForeignCurrencyContractIdentifierAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Open Forward Foreign Currency Contract, Identifier [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OpenForwardForeignCurrencyContractIdentifierAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OpenForwardForeignCurrencyContractIdentifierAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OpenForwardForeignCurrencyContractIdentifierAxis" xlink:to="lab_us-gaap_OpenForwardForeignCurrencyContractIdentifierAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredDebtMember_019fd71c-09af-7cc8-a5a2-7224fe8f5c98_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Loan</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_019fd71c-09af-7917-aeb2-eeb4db70a0b7_verboseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Secured debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebtMember" xlink:to="lab_us-gaap_SecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019fd71c-09af-73c2-bcc9-99b326d1aa49_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019fd71c-09ae-7b68-9a58-b8cb76e6fb5a_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total net assets</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019fd71c-09ae-727c-85df-6fe3454a8711_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019fd71c-09ae-71e5-b2ef-c2c1a4508933_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019fd71c-09ae-7bb5-bd16-490dfca75cc3_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net assets, end of period</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019fd71c-09ae-79e8-8d98-c672c6952eb3_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations_019fd71c-09af-76ec-8ed7-6a1511ac4e1a_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable from broker</link:label>
    <link:label id="lab_us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations_label_en-US" xlink:label="lab_us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable from Broker-Dealer and Clearing Organization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivablesFromBrokersDealersAndClearingOrganizations"/>
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    <link:label id="lab_bxsl_InvestmentCompanyExpenseRatioBeforeFeeWaiverAndReimbursements_label_en-US" xlink:label="lab_bxsl_InvestmentCompanyExpenseRatioBeforeFeeWaiverAndReimbursements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Expense Ratio Before Fee Waiver And Reimbursements</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyExpenseRatioBeforeFeeWaiverAndReimbursements_documentation_en-US" xlink:label="lab_bxsl_InvestmentCompanyExpenseRatioBeforeFeeWaiverAndReimbursements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Expense Ratio Before Fee Waiver And Reimbursements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentCompanyExpenseRatioBeforeFeeWaiverAndReimbursements" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentCompanyExpenseRatioBeforeFeeWaiverAndReimbursements"/>
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    <link:label id="lab_us-gaap_ProfessionalFees_019fd71c-091c-786b-8360-8d2906c39275_terseLabel_en-US" xlink:label="lab_us-gaap_ProfessionalFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Professional fees</link:label>
    <link:label id="lab_us-gaap_ProfessionalFees_label_en-US" xlink:label="lab_us-gaap_ProfessionalFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Professional Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfessionalFees" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfessionalFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfessionalFees" xlink:to="lab_us-gaap_ProfessionalFees" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIssuerAffiliationDomain_019fd71c-09af-7f68-977e-673dbd5da36e_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIssuerAffiliationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Issuer Affiliation [Domain]</link:label>
    <link:label id="lab_us-gaap_InvestmentIssuerAffiliationDomain_label_en-US" xlink:label="lab_us-gaap_InvestmentIssuerAffiliationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Issuer Affiliation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIssuerAffiliationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIssuerAffiliationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIssuerAffiliationDomain" xlink:to="lab_us-gaap_InvestmentIssuerAffiliationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019fd71c-091c-7548-9160-445e4d642a4c_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A2023NotesMember_label_en-US" xlink:label="lab_bxsl_A2023NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2023 Notes [Member]</link:label>
    <link:label id="lab_bxsl_A2023NotesMember_documentation_en-US" xlink:label="lab_bxsl_A2023NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2023 Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A2023NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_A2023NotesMember"/>
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    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
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    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019fd71c-09ae-7814-a844-ce5b76321c5a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsLineItems_019fd71c-09af-7649-a191-c6a9c46a25c8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare_019fd71c-09af-7a19-9afc-014f74db3722_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net change in unrealized and realized gain (loss) (in usd per share)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Gain (Loss) on Investment, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyGainLossOnInvestmentPerShare"/>
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    <link:label id="lab_bxsl_MaterialHoldingsLLC2Member_019fd71c-091c-71c0-b5d7-7f19fd5edb1b_terseLabel_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLC2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLC2Member_label_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLC2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC 2 [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLC2Member_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLC2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingsLLC2Member" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingsLLC2Member"/>
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    <link:label id="lab_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTax_label_en-US" xlink:label="lab_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss), Investment and Derivative, Operating, and Foreign Currency Transaction, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealizedAndUnrealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionOperatingAfterTax"/>
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    <link:label id="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt2Member_019fd71c-0a16-7910-a724-7308d2b7954b_terseLabel_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - First Lien Debt</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt2Member_label_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - First Lien Debt 2 [Member]</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt2Member_documentation_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - First Lien Debt 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AlignPrecisionGroupLLCFirstLienDebt2Member" xlink:href="bxsl-20260930.xsd#bxsl_AlignPrecisionGroupLLCFirstLienDebt2Member"/>
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    <link:label id="lab_us-gaap_DebtAndEquitySecuritiesUnrealizedGainLoss_019fd71c-09af-7cec-b40c-9a3e41a35e8c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtAndEquitySecuritiesUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net change in unrealized (appreciation) depreciation on investments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtAndEquitySecuritiesUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtAndEquitySecuritiesUnrealizedGainLoss"/>
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    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
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    <link:label id="lab_bxsl_DistributorsSectorMember_019fd71c-0a16-7428-9b0b-b3cb27f4af6f_terseLabel_en-US" xlink:label="lab_bxsl_DistributorsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributors</link:label>
    <link:label id="lab_bxsl_DistributorsSectorMember_label_en-US" xlink:label="lab_bxsl_DistributorsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Distributors Sector [Member]</link:label>
    <link:label id="lab_bxsl_DistributorsSectorMember_documentation_en-US" xlink:label="lab_bxsl_DistributorsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Distributors Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DistributorsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_DistributorsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DistributorsSectorMember" xlink:to="lab_bxsl_DistributorsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateDomain_019fd71c-091c-7ed0-84b0-2c97a06aae7c_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:label id="lab_us-gaap_VariableRateDomain_label_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableRateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateDomain" xlink:to="lab_us-gaap_VariableRateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIssuerNameDomain_019fd71c-09ae-72d9-9f48-75705a220c45_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIssuerNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Issuer Name [Domain]</link:label>
    <link:label id="lab_us-gaap_InvestmentIssuerNameDomain_label_en-US" xlink:label="lab_us-gaap_InvestmentIssuerNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Issuer Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIssuerNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIssuerNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIssuerNameDomain" xlink:to="lab_us-gaap_InvestmentIssuerNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividends_019fd71c-09af-7eee-a81c-fb720df6dcd0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid in cash</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividends" xlink:to="lab_us-gaap_PaymentsOfDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019fd71c-091c-77b6-9aaf-233c30e049b3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtAndEquitySecuritiesRealizedGainLoss_019fd71c-09af-7f1b-9859-e40527c0c45b_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtAndEquitySecuritiesRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Non-controlled/non-affiliated investments</link:label>
    <link:label id="lab_us-gaap_DebtAndEquitySecuritiesRealizedGainLoss_019fd71c-09af-7339-97e9-d38060f0476b_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtAndEquitySecuritiesRealizedGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net realized (gain) loss on investments</link:label>
    <link:label id="lab_us-gaap_DebtAndEquitySecuritiesRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtAndEquitySecuritiesRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt and Equity Securities, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtAndEquitySecuritiesRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtAndEquitySecuritiesRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtAndEquitySecuritiesRealizedGainLoss" xlink:to="lab_us-gaap_DebtAndEquitySecuritiesRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MaterialHoldingsLLC3Member_019fd71c-091c-7442-9951-3674c47504b5_terseLabel_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLC3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLC3Member_label_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLC3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC 3 [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLC3Member_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLC3Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingsLLC3Member" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingsLLC3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MaterialHoldingsLLC3Member" xlink:to="lab_bxsl_MaterialHoldingsLLC3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019fd71c-09af-7364-9c6e-4d7a7912208c_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019fd71c-09ae-7455-86a9-5c4a3ed2df8f_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_019fd71c-09ae-776f-bccd-7027ffb32139_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember_019fd71c-09ae-7b96-a586-15ba90b4d3f7_terseLabel_en-US" xlink:label="lab_bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Electronic Equipment, Instruments &amp; Components</link:label>
    <link:label id="lab_bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember_label_en-US" xlink:label="lab_bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Electronic Equipment, Instruments &amp; Components Sector [Member]</link:label>
    <link:label id="lab_bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember_documentation_en-US" xlink:label="lab_bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Electronic Equipment, Instruments &amp; Components Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember" xlink:to="lab_bxsl_ElectronicEquipmentInstrumentsComponentsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_New2027NotesMember_019fd71c-09ae-7630-ab6f-c1e44a548c72_terseLabel_en-US" xlink:label="lab_bxsl_New2027NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">November 2027 Notes</link:label>
    <link:label id="lab_bxsl_New2027NotesMember_label_en-US" xlink:label="lab_bxsl_New2027NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New 2027 Notes [Member]</link:label>
    <link:label id="lab_bxsl_New2027NotesMember_documentation_en-US" xlink:label="lab_bxsl_New2027NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New 2027 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_New2027NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_New2027NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_New2027NotesMember" xlink:to="lab_bxsl_New2027NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesByIndustryAxis_019fd71c-091c-7b20-998d-08eb0e8281c0_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesByIndustryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industry Sector [Axis]</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesByIndustryAxis_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesByIndustryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industry Sector [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesByIndustryAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesByIndustryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesByIndustryAxis" xlink:to="lab_us-gaap_EquitySecuritiesByIndustryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MedalliaTopcoLLCEquityAndOtherSeniorPreferredUnitsMember_01a186f3-12b0-7bac-8855-4f4db6df7ccf_terseLabel_en-US" xlink:label="lab_bxsl_MedalliaTopcoLLCEquityAndOtherSeniorPreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Medallia Topco, LLC - Equity and other - Senior Preferred Units</link:label>
    <link:label id="lab_bxsl_MedalliaTopcoLLCEquityAndOtherSeniorPreferredUnitsMember_label_en-US" xlink:label="lab_bxsl_MedalliaTopcoLLCEquityAndOtherSeniorPreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Medallia Topco, LLC - Equity and other - Senior Preferred Units [Member]</link:label>
    <link:label id="lab_bxsl_MedalliaTopcoLLCEquityAndOtherSeniorPreferredUnitsMember_documentation_en-US" xlink:label="lab_bxsl_MedalliaTopcoLLCEquityAndOtherSeniorPreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Medallia Topco, LLC - Equity and other - Senior Preferred Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MedalliaTopcoLLCEquityAndOtherSeniorPreferredUnitsMember" xlink:href="bxsl-20260930.xsd#bxsl_MedalliaTopcoLLCEquityAndOtherSeniorPreferredUnitsMember"/>
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    <link:label id="lab_bxsl_AdministrationAgreementMember_019fd71c-0a16-786c-83f3-4dd7cbee5701_terseLabel_en-US" xlink:label="lab_bxsl_AdministrationAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administration Agreement</link:label>
    <link:label id="lab_bxsl_AdministrationAgreementMember_label_en-US" xlink:label="lab_bxsl_AdministrationAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administration Agreement [Member]</link:label>
    <link:label id="lab_bxsl_AdministrationAgreementMember_documentation_en-US" xlink:label="lab_bxsl_AdministrationAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Administration Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AdministrationAgreementMember" xlink:href="bxsl-20260930.xsd#bxsl_AdministrationAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AdministrationAgreementMember" xlink:to="lab_bxsl_AdministrationAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_VariableRateScenarioAxis_019fd71c-09af-7bfe-a4a0-540f8bbda967_terseLabel_en-US" xlink:label="lab_bxsl_VariableRateScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate Scenario [Axis]</link:label>
    <link:label id="lab_bxsl_VariableRateScenarioAxis_label_en-US" xlink:label="lab_bxsl_VariableRateScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate Scenario [Axis]</link:label>
    <link:label id="lab_bxsl_VariableRateScenarioAxis_documentation_en-US" xlink:label="lab_bxsl_VariableRateScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Rate Scenario</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_VariableRateScenarioAxis" xlink:href="bxsl-20260930.xsd#bxsl_VariableRateScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_VariableRateScenarioAxis" xlink:to="lab_bxsl_VariableRateScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyExciseTaxExpense_019fd71c-0a16-77e0-bffc-5986909af0ec_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyExciseTaxExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excise tax expense</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyExciseTaxExpense_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyExciseTaxExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Excise Tax Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyExciseTaxExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyExciseTaxExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyExciseTaxExpense" xlink:to="lab_us-gaap_InvestmentCompanyExciseTaxExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ManagementAndServiceFeesRate_019fd71c-09ae-73af-b8b8-954d889693e3_terseLabel_en-US" xlink:label="lab_us-gaap_ManagementAndServiceFeesRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fee rate</link:label>
    <link:label id="lab_us-gaap_ManagementAndServiceFeesRate_label_en-US" xlink:label="lab_us-gaap_ManagementAndServiceFeesRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management and Service Fees, Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementAndServiceFeesRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ManagementAndServiceFeesRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ManagementAndServiceFeesRate" xlink:to="lab_us-gaap_ManagementAndServiceFeesRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValuePeriodIncreaseDecrease_019fd71c-09ae-7382-937e-63e914c3b650_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValuePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Change in Unrealized Gains (Losses)</link:label>
    <link:label id="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValuePeriodIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValuePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in and Advances to Affiliates, at Fair Value, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValuePeriodIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValuePeriodIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValuePeriodIncreaseDecrease" xlink:to="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValuePeriodIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_019fd71c-09af-70de-b8f0-47b568f0c24f_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributable Earnings (Loss)</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_019fd71c-09af-7509-889f-1ec55a72300d_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_019fd71c-09af-7334-9c16-00a23597f8a1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:to="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare_019fd71c-09af-7acc-a706-ab3421ca4b98_totalLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in net assets resulting from operations (in usd per share)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Investment Income (Loss) from Operations, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:to="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019fd71c-09af-7d3f-aace-06676e4f68fb_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019fd71c-09af-7c50-8c71-feab941afdf5_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Shares outstanding, end of period</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019fd71c-09af-7e06-88a9-a9d4ebab413d_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings (loss) per share diluted (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019fd71c-09af-7804-b311-20892d519f1e_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Earnings (loss) per common share diluted (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_TradingCompaniesDistributorsSectorMember_019fd71c-091c-7c79-adfd-ebe2575fb994_terseLabel_en-US" xlink:label="lab_bxsl_TradingCompaniesDistributorsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Companies &amp; Distributors</link:label>
    <link:label id="lab_bxsl_TradingCompaniesDistributorsSectorMember_label_en-US" xlink:label="lab_bxsl_TradingCompaniesDistributorsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Companies &amp; Distributors Sector [Member]</link:label>
    <link:label id="lab_bxsl_TradingCompaniesDistributorsSectorMember_documentation_en-US" xlink:label="lab_bxsl_TradingCompaniesDistributorsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Trading Companies &amp; Distributors Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_TradingCompaniesDistributorsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_TradingCompaniesDistributorsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_TradingCompaniesDistributorsSectorMember" xlink:to="lab_bxsl_TradingCompaniesDistributorsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeOperatingPaidInCash_019fd71c-09af-78ef-aaf8-3491352a9ff5_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeOperatingPaidInCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeOperatingPaidInCash_label_en-US" xlink:label="lab_us-gaap_InterestIncomeOperatingPaidInCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Operating, Paid in Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeOperatingPaidInCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeOperatingPaidInCash"/>
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    <link:label id="lab_bxsl_November2027NotesMember_label_en-US" xlink:label="lab_bxsl_November2027NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">November 2027 Notes [Member]</link:label>
    <link:label id="lab_bxsl_November2027NotesMember_documentation_en-US" xlink:label="lab_bxsl_November2027NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">November 2027 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_November2027NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_November2027NotesMember"/>
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    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_019fd71c-0a16-7123-a578-6fc22b940410_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Offsetting Assets</link:label>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:to="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShareDiluted_019fd71c-09ae-7d24-8e53-c6553d2932eb_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income, diluted (in usd per share)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Investment Income (Loss), Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShareDiluted" xlink:to="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MaterialHoldingsLLC1Member_019fd71c-09af-7d23-9ecc-5b44aced2506_terseLabel_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLC1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLC1Member_label_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLC1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC 1 [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLC1Member_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLC1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingsLLC1Member" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingsLLC1Member"/>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_019fd71c-09ae-7d30-b502-85ddc1240a5f_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount available</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A2026NotesMember_019fd71c-09af-750b-9786-771971f430fd_terseLabel_en-US" xlink:label="lab_bxsl_A2026NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 Notes</link:label>
    <link:label id="lab_bxsl_A2026NotesMember_label_en-US" xlink:label="lab_bxsl_A2026NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2026 Notes [Member]</link:label>
    <link:label id="lab_bxsl_A2026NotesMember_documentation_en-US" xlink:label="lab_bxsl_A2026NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2026 Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A2026NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_A2026NotesMember"/>
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    <link:label id="lab_us-gaap_InvestmentCompanyTotalReturnMarketValue_019fd71c-091c-74c9-aa89-774241c8b0d6_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyTotalReturnMarketValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total return based on market value</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyTotalReturnMarketValue_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyTotalReturnMarketValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Total Return, Market Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyTotalReturnMarketValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyTotalReturnMarketValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyTotalReturnMarketValue" xlink:to="lab_us-gaap_InvestmentCompanyTotalReturnMarketValue" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_019fd71c-09af-7a4b-bcd5-e4227be2b979_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Interest Payable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInInterestPayableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:to="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_019fd71c-09ae-72b4-aaa9-5d443984c0b9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from principal repayments and sales of investments</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_O2026Q4DividendsMember_01a198ab-8fd6-7a32-a692-b457c96cd211_terseLabel_en-US" xlink:label="lab_bxsl_O2026Q4DividendsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">O 2026 Q4 Dividends</link:label>
    <link:label id="lab_bxsl_O2026Q4DividendsMember_label_en-US" xlink:label="lab_bxsl_O2026Q4DividendsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">O 2026 Q4 Dividends [Member]</link:label>
    <link:label id="lab_bxsl_O2026Q4DividendsMember_documentation_en-US" xlink:label="lab_bxsl_O2026Q4DividendsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">O 2026 Q4 Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_O2026Q4DividendsMember" xlink:href="bxsl-20260930.xsd#bxsl_O2026Q4DividendsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_O2026Q4DividendsMember" xlink:to="lab_bxsl_O2026Q4DividendsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIssuerNameAxis_019fd71c-09af-7a10-96fe-4b04050a1b2e_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIssuerNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Issuer Name [Axis]</link:label>
    <link:label id="lab_us-gaap_InvestmentIssuerNameAxis_label_en-US" xlink:label="lab_us-gaap_InvestmentIssuerNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Issuer Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIssuerNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIssuerNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIssuerNameAxis" xlink:to="lab_us-gaap_InvestmentIssuerNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssued1_019fd71c-09ae-7fb0-8398-c88c2a0586ce_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinvestment of distributions during the period</link:label>
    <link:label id="lab_us-gaap_StockIssued1_label_en-US" xlink:label="lab_us-gaap_StockIssued1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssued1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssued1" xlink:to="lab_us-gaap_StockIssued1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_019fd71c-09af-7a8d-88d1-9f272b214fb0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_FinancialServicesOtherSectorMember_019fd71c-09ae-7ea7-af63-1a6f6745e53a_terseLabel_en-US" xlink:label="lab_bxsl_FinancialServicesOtherSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Services</link:label>
    <link:label id="lab_bxsl_FinancialServicesOtherSectorMember_label_en-US" xlink:label="lab_bxsl_FinancialServicesOtherSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Services, Other Sector [Member]</link:label>
    <link:label id="lab_bxsl_FinancialServicesOtherSectorMember_documentation_en-US" xlink:label="lab_bxsl_FinancialServicesOtherSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Services, Other Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_FinancialServicesOtherSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_FinancialServicesOtherSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_FinancialServicesOtherSectorMember" xlink:to="lab_bxsl_FinancialServicesOtherSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_019fd71c-09ae-74ce-b3d8-5be1badbd2f7_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember_01a186f2-2ed7-7659-b12c-5e9ee347a8e5_terseLabel_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class A Units</link:label>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember_label_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class A Units [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class A Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember" xlink:to="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsDeclaredTableTextBlock_019fd71c-09af-73d6-bbb5-1e22a1abd82d_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsDeclaredTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Dividends Declared</link:label>
    <link:label id="lab_us-gaap_DividendsDeclaredTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DividendsDeclaredTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Declared [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsDeclaredTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsDeclaredTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsDeclaredTableTextBlock" xlink:to="lab_us-gaap_DividendsDeclaredTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_019fd71c-09ae-7f53-bc42-4215ae41f70e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings on debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_019fd71c-09ae-75a4-92af-f3d7c3122d7d_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain" xlink:to="lab_us-gaap_RelatedPartyTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InterestRateSwap1Member_019fd71c-09af-7373-b3fc-e5411b0046f8_terseLabel_en-US" xlink:label="lab_bxsl_InterestRateSwap1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 1</link:label>
    <link:label id="lab_bxsl_InterestRateSwap1Member_label_en-US" xlink:label="lab_bxsl_InterestRateSwap1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 1 [Member]</link:label>
    <link:label id="lab_bxsl_InterestRateSwap1Member_documentation_en-US" xlink:label="lab_bxsl_InterestRateSwap1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InterestRateSwap1Member" xlink:href="bxsl-20260930.xsd#bxsl_InterestRateSwap1Member"/>
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    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealizedAfterTax_019fd71c-091c-7ab9-9c19-f2737d0c1f36_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealizedAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Translation of assets and liabilities in foreign currencies</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealizedAfterTax_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealizedAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss), Foreign Currency Transaction, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossUnrealizedAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainLossUnrealizedAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionGainLossUnrealizedAfterTax" xlink:to="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealizedAfterTax" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
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    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_019fd71c-091c-77dc-92ba-a79edc79c638_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments at fair value</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_019fd71c-091c-7007-a264-186c2f4f193b_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_019fd71c-091c-7e7e-84d2-50523713ddac_periodStartLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_019fd71c-091c-70e8-ba74-2661b660cf10_periodEndLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_label_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentOwnedAtFairValue"/>
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    <link:label id="lab_us-gaap_EquitySecuritiesMember_019fd71c-091c-7898-9264-79f74d42e156_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments in equity</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesMember_019fd71c-091c-7cdc-b141-aad7d9b9b298_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesMember_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesMember" xlink:to="lab_us-gaap_EquitySecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdministrativeFeesExpense_019fd71c-09af-7e74-9256-2b13723fa1bc_terseLabel_en-US" xlink:label="lab_us-gaap_AdministrativeFeesExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative service expenses (Note 3)</link:label>
    <link:label id="lab_us-gaap_AdministrativeFeesExpense_label_en-US" xlink:label="lab_us-gaap_AdministrativeFeesExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administrative Fees Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdministrativeFeesExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdministrativeFeesExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdministrativeFeesExpense" xlink:to="lab_us-gaap_AdministrativeFeesExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019fd71c-09af-7e98-abc6-a41150635ec1_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019fd71c-09af-7935-8222-c45e208baf7c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value, beginning of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019fd71c-09af-780d-97c5-19d054ad60bb_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Fair value, end of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DistributionCostsIncurredButNotYetPaid_019fd71c-09ae-7634-9418-c5341fa1ba47_terseLabel_en-US" xlink:label="lab_bxsl_DistributionCostsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distribution payable</link:label>
    <link:label id="lab_bxsl_DistributionCostsIncurredButNotYetPaid_label_en-US" xlink:label="lab_bxsl_DistributionCostsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Distribution Costs Incurred But Not Yet Paid</link:label>
    <link:label id="lab_bxsl_DistributionCostsIncurredButNotYetPaid_documentation_en-US" xlink:label="lab_bxsl_DistributionCostsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Distribution Costs Incurred But Not Yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DistributionCostsIncurredButNotYetPaid" xlink:href="bxsl-20260930.xsd#bxsl_DistributionCostsIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DistributionCostsIncurredButNotYetPaid" xlink:to="lab_bxsl_DistributionCostsIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ProfessionalServicesSectorMember_019fd71c-09af-7358-84e5-c17e290d2682_terseLabel_en-US" xlink:label="lab_bxsl_ProfessionalServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Professional Services</link:label>
    <link:label id="lab_bxsl_ProfessionalServicesSectorMember_label_en-US" xlink:label="lab_bxsl_ProfessionalServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Professional Services Sector [Member]</link:label>
    <link:label id="lab_bxsl_ProfessionalServicesSectorMember_documentation_en-US" xlink:label="lab_bxsl_ProfessionalServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Professional Services Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ProfessionalServicesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_ProfessionalServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ProfessionalServicesSectorMember" xlink:to="lab_bxsl_ProfessionalServicesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_September2029NotesMember_019fd71c-0a16-7fbd-aba2-f1ef03b82155_terseLabel_en-US" xlink:label="lab_bxsl_September2029NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">September 2029 Notes</link:label>
    <link:label id="lab_bxsl_September2029NotesMember_label_en-US" xlink:label="lab_bxsl_September2029NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">September 2029 Notes [Member]</link:label>
    <link:label id="lab_bxsl_September2029NotesMember_documentation_en-US" xlink:label="lab_bxsl_September2029NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">September 2029 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_September2029NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_September2029NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_September2029NotesMember" xlink:to="lab_bxsl_September2029NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMember_019fd71c-09af-779c-8d5e-f786d15dc2f0_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMember_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMember" xlink:to="lab_us-gaap_LongTermDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_O2027Q1DividendsMember_01a198ab-b3bf-7563-b23a-593adba3dd72_terseLabel_en-US" xlink:label="lab_bxsl_O2027Q1DividendsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">O 2027 Q1 Dividends</link:label>
    <link:label id="lab_bxsl_O2027Q1DividendsMember_label_en-US" xlink:label="lab_bxsl_O2027Q1DividendsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">O 2027 Q1 Dividends [Member]</link:label>
    <link:label id="lab_bxsl_O2027Q1DividendsMember_documentation_en-US" xlink:label="lab_bxsl_O2027Q1DividendsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">O 2027 Q1 Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_O2027Q1DividendsMember" xlink:href="bxsl-20260930.xsd#bxsl_O2027Q1DividendsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_O2027Q1DividendsMember" xlink:to="lab_bxsl_O2027Q1DividendsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InterestRateSwap3Member_019fd71c-09af-7e9b-bbfe-d01ea294d896_terseLabel_en-US" xlink:label="lab_bxsl_InterestRateSwap3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 3</link:label>
    <link:label id="lab_bxsl_InterestRateSwap3Member_label_en-US" xlink:label="lab_bxsl_InterestRateSwap3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 3 [Member]</link:label>
    <link:label id="lab_bxsl_InterestRateSwap3Member_documentation_en-US" xlink:label="lab_bxsl_InterestRateSwap3Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InterestRateSwap3Member" xlink:href="bxsl-20260930.xsd#bxsl_InterestRateSwap3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InterestRateSwap3Member" xlink:to="lab_bxsl_InterestRateSwap3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsAxis_019fd71c-09ae-7ce3-a4fc-7324aae93645_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Axis]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsAxis_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsAxis" xlink:to="lab_us-gaap_OtherCommitmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueNetAbstract_019fd71c-09ae-7fed-a8cb-01b05d143fb8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueNetAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset of Collateral [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetFairValueNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:to="lab_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InterestRateSwap6Member_019fd71c-0a16-7c7d-b533-27651abcfc02_terseLabel_en-US" xlink:label="lab_bxsl_InterestRateSwap6Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 6</link:label>
    <link:label id="lab_bxsl_InterestRateSwap6Member_label_en-US" xlink:label="lab_bxsl_InterestRateSwap6Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 6 [Member]</link:label>
    <link:label id="lab_bxsl_InterestRateSwap6Member_documentation_en-US" xlink:label="lab_bxsl_InterestRateSwap6Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 6</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InterestRateSwap6Member" xlink:href="bxsl-20260930.xsd#bxsl_InterestRateSwap6Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InterestRateSwap6Member" xlink:to="lab_bxsl_InterestRateSwap6Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentOwnedNonaccrualNumberOfLoans_019fd71c-09af-7dd1-9134-7aa6a9e7d470_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentOwnedNonaccrualNumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of loans in non-accrual status</link:label>
    <link:label id="lab_bxsl_InvestmentOwnedNonaccrualNumberOfLoans_label_en-US" xlink:label="lab_bxsl_InvestmentOwnedNonaccrualNumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Nonaccrual, Number Of Loans</link:label>
    <link:label id="lab_bxsl_InvestmentOwnedNonaccrualNumberOfLoans_documentation_en-US" xlink:label="lab_bxsl_InvestmentOwnedNonaccrualNumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Owned, Nonaccrual, Number Of Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentOwnedNonaccrualNumberOfLoans" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentOwnedNonaccrualNumberOfLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentOwnedNonaccrualNumberOfLoans" xlink:to="lab_bxsl_InvestmentOwnedNonaccrualNumberOfLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_NewACIBuyerLLCFirstLienDebt2Member_019fd71c-0a16-7e8a-a9dd-6c992ccba17c_terseLabel_en-US" xlink:label="lab_bxsl_NewACIBuyerLLCFirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New ACI Buyer, LLC - First Lien Debt</link:label>
    <link:label id="lab_bxsl_NewACIBuyerLLCFirstLienDebt2Member_label_en-US" xlink:label="lab_bxsl_NewACIBuyerLLCFirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New ACI Buyer, LLC - First Lien Debt 2 [Member]</link:label>
    <link:label id="lab_bxsl_NewACIBuyerLLCFirstLienDebt2Member_documentation_en-US" xlink:label="lab_bxsl_NewACIBuyerLLCFirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New ACI Buyer, LLC - First Lien Debt 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_NewACIBuyerLLCFirstLienDebt2Member" xlink:href="bxsl-20260930.xsd#bxsl_NewACIBuyerLLCFirstLienDebt2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_NewACIBuyerLLCFirstLienDebt2Member" xlink:to="lab_bxsl_NewACIBuyerLLCFirstLienDebt2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_019fd71c-09af-74b2-8973-4fc7fa8cc137_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPricePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit_019fd71c-09af-7641-aadc-e69d92465aa2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax (provision) benefit</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss), Investment and Derivative, Operating, Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:to="lab_us-gaap_UnrealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019fd71c-09af-7959-b046-b1b27459e5e3_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019fd71c-09af-732c-b855-7536397ec82d_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember_019fd71c-09ae-7b94-ae3d-c693de5fda14_terseLabel_en-US" xlink:label="lab_bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, First Lien, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, First Lien, Unrealized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, First Lien, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember" xlink:to="lab_bxsl_DebtSecuritiesFirstLienUnrealizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeOperatingPaidInKind_019fd71c-091c-762a-8d4f-cff380bca134_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeOperatingPaidInKind" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payment-in-kind interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeOperatingPaidInKind_label_en-US" xlink:label="lab_us-gaap_InterestIncomeOperatingPaidInKind" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Operating, Paid in Kind</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeOperatingPaidInKind" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeOperatingPaidInKind"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeOperatingPaidInKind" xlink:to="lab_us-gaap_InterestIncomeOperatingPaidInKind" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_BERMUDAAndCAYMANISLANDMember_019fd71c-091c-7d97-8f4b-fe68c760daa3_terseLabel_en-US" xlink:label="lab_bxsl_BERMUDAAndCAYMANISLANDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bermuda/Cayman Islands</link:label>
    <link:label id="lab_bxsl_BERMUDAAndCAYMANISLANDMember_label_en-US" xlink:label="lab_bxsl_BERMUDAAndCAYMANISLANDMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BERMUDA and CAYMAN ISLAND [Member]</link:label>
    <link:label id="lab_bxsl_BERMUDAAndCAYMANISLANDMember_documentation_en-US" xlink:label="lab_bxsl_BERMUDAAndCAYMANISLANDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BERMUDA and CAYMAN ISLAND</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_BERMUDAAndCAYMANISLANDMember" xlink:href="bxsl-20260930.xsd#bxsl_BERMUDAAndCAYMANISLANDMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_BERMUDAAndCAYMANISLANDMember" xlink:to="lab_bxsl_BERMUDAAndCAYMANISLANDMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OpenForwardForeignCurrencyContractTable_019fd71c-09af-7037-be5f-b7f95fe25ee6_terseLabel_en-US" xlink:label="lab_us-gaap_OpenForwardForeignCurrencyContractTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Open Forward Foreign Currency Contract [Table]</link:label>
    <link:label id="lab_us-gaap_OpenForwardForeignCurrencyContractTable_label_en-US" xlink:label="lab_us-gaap_OpenForwardForeignCurrencyContractTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Open Forward Foreign Currency Contract [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OpenForwardForeignCurrencyContractTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OpenForwardForeignCurrencyContractTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OpenForwardForeignCurrencyContractTable" xlink:to="lab_us-gaap_OpenForwardForeignCurrencyContractTable" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_DerivativeAndForeignCurrencyTransactionPriceChangeUnrealizedGainLossOperatingBeforeTax_label_en-US" xlink:label="lab_us-gaap_DerivativeAndForeignCurrencyTransactionPriceChangeUnrealizedGainLossOperatingBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss), Derivative and Foreign Currency Transaction Price Change, Operating, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAndForeignCurrencyTransactionPriceChangeUnrealizedGainLossOperatingBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAndForeignCurrencyTransactionPriceChangeUnrealizedGainLossOperatingBeforeTax"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
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    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019fd71c-09af-7f11-a828-81cee178427c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCEquityAndOtherClassA3UnitsMember_01a186f0-325d-7ca2-b46a-d9b57d1d785c_terseLabel_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCEquityAndOtherClassA3UnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - Equity and other - Class A-3 Units</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCEquityAndOtherClassA3UnitsMember_label_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCEquityAndOtherClassA3UnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - Equity and other - Class A-3 Units [Member]</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCEquityAndOtherClassA3UnitsMember_documentation_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCEquityAndOtherClassA3UnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - Equity and other - Class A-3 Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AlignPrecisionGroupLLCEquityAndOtherClassA3UnitsMember" xlink:href="bxsl-20260930.xsd#bxsl_AlignPrecisionGroupLLCEquityAndOtherClassA3UnitsMember"/>
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    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019fd71c-0a16-7f56-852c-3b7e9b367601_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
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    <link:label id="lab_srt_StatementGeographicalAxis_019fd71c-09af-7211-ad19-d6e58aad7e1e_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementGeographicalAxis"/>
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    <link:label id="lab_us-gaap_InvestmentIssuerAffiliationAxis_019fd71c-09af-78fc-9dfe-4559efd75d1f_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIssuerAffiliationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Issuer Affiliation [Axis]</link:label>
    <link:label id="lab_us-gaap_InvestmentIssuerAffiliationAxis_label_en-US" xlink:label="lab_us-gaap_InvestmentIssuerAffiliationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Issuer Affiliation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIssuerAffiliationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIssuerAffiliationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIssuerAffiliationAxis" xlink:to="lab_us-gaap_InvestmentIssuerAffiliationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019fd71c-091c-701f-8eb2-2b03585bd9ff_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgedLiabilityFairValueHedge_019fd71c-09af-7ef6-99b8-692d238f05f3_terseLabel_en-US" xlink:label="lab_us-gaap_HedgedLiabilityFairValueHedge" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_HedgedLiabilityFairValueHedge_label_en-US" xlink:label="lab_us-gaap_HedgedLiabilityFairValueHedge" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Liability, Fair Value Hedge</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgedLiabilityFairValueHedge" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgedLiabilityFairValueHedge"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgedLiabilityFairValueHedge" xlink:to="lab_us-gaap_HedgedLiabilityFairValueHedge" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_019fd71c-091c-7bdf-8e19-1780e4e6b205_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ValuationAssetRecoverabilityMember_019fd71c-091c-79b9-816e-e6d3bb4c9801_terseLabel_en-US" xlink:label="lab_bxsl_ValuationAssetRecoverabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Recoverability</link:label>
    <link:label id="lab_bxsl_ValuationAssetRecoverabilityMember_label_en-US" xlink:label="lab_bxsl_ValuationAssetRecoverabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation, Asset Recoverability [Member]</link:label>
    <link:label id="lab_bxsl_ValuationAssetRecoverabilityMember_documentation_en-US" xlink:label="lab_bxsl_ValuationAssetRecoverabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation, Asset Recoverability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ValuationAssetRecoverabilityMember" xlink:href="bxsl-20260930.xsd#bxsl_ValuationAssetRecoverabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ValuationAssetRecoverabilityMember" xlink:to="lab_bxsl_ValuationAssetRecoverabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InteractiveMediaServicesSectorMember_019fd71c-09af-7e29-8494-2db842233c02_terseLabel_en-US" xlink:label="lab_bxsl_InteractiveMediaServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interactive Media &amp; Services</link:label>
    <link:label id="lab_bxsl_InteractiveMediaServicesSectorMember_label_en-US" xlink:label="lab_bxsl_InteractiveMediaServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interactive Media &amp; Services Sector [Member]</link:label>
    <link:label id="lab_bxsl_InteractiveMediaServicesSectorMember_documentation_en-US" xlink:label="lab_bxsl_InteractiveMediaServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interactive Media &amp; Services Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InteractiveMediaServicesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_InteractiveMediaServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InteractiveMediaServicesSectorMember" xlink:to="lab_bxsl_InteractiveMediaServicesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019fd71c-091c-7524-85d5-e348e3a3078c_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents (including restricted cash), beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019fd71c-091c-751a-8664-3b5e05a6789a_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents (including restricted cash), end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_019fd71c-0a16-70b7-b0a8-016841eb2885_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash collateral pledged not offset</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralRightToReclaimCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:to="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLC1Member_019fd71c-091c-75e4-8c8a-9d9f0de90216_terseLabel_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLC1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLC1Member_label_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLC1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC 1 [Member]</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLC1Member_documentation_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLC1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AlignPrecisionGroupLLC1Member" xlink:href="bxsl-20260930.xsd#bxsl_AlignPrecisionGroupLLC1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AlignPrecisionGroupLLC1Member" xlink:to="lab_bxsl_AlignPrecisionGroupLLC1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements_019fd71c-09af-7b2d-93c9-43c00a0a4c86_terseLabel_en-US" xlink:label="lab_bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of deferred financing costs</link:label>
    <link:label id="lab_bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements_label_en-US" xlink:label="lab_bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization Of Debt Issuance Costs, Line Of Credit Arrangements</link:label>
    <link:label id="lab_bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements_documentation_en-US" xlink:label="lab_bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amortization Of Debt Issuance Costs, Line Of Credit Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements" xlink:href="bxsl-20260930.xsd#bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements" xlink:to="lab_bxsl_AmortizationOfDebtIssuanceCostsLineOfCreditArrangements" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_CommitmentFeeScenarioDomain_019fd71c-0a16-73c1-8c8e-936f06919d4d_terseLabel_en-US" xlink:label="lab_bxsl_CommitmentFeeScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitment Fee Scenario [Domain]</link:label>
    <link:label id="lab_bxsl_CommitmentFeeScenarioDomain_label_en-US" xlink:label="lab_bxsl_CommitmentFeeScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitment Fee Scenario [Domain]</link:label>
    <link:label id="lab_bxsl_CommitmentFeeScenarioDomain_documentation_en-US" xlink:label="lab_bxsl_CommitmentFeeScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commitment Fee Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_CommitmentFeeScenarioDomain" xlink:href="bxsl-20260930.xsd#bxsl_CommitmentFeeScenarioDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_CommitmentFeeScenarioDomain" xlink:to="lab_bxsl_CommitmentFeeScenarioDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MeasurementInputDiscountExpectedToProceedsMember_01a174b4-1f9d-7a8e-a13b-464b08615ffd_terseLabel_en-US" xlink:label="lab_bxsl_MeasurementInputDiscountExpectedToProceedsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount to Expected Proceeds</link:label>
    <link:label id="lab_bxsl_MeasurementInputDiscountExpectedToProceedsMember_label_en-US" xlink:label="lab_bxsl_MeasurementInputDiscountExpectedToProceedsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Expected to Proceeds [Member]</link:label>
    <link:label id="lab_bxsl_MeasurementInputDiscountExpectedToProceedsMember_documentation_en-US" xlink:label="lab_bxsl_MeasurementInputDiscountExpectedToProceedsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Expected to Proceeds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MeasurementInputDiscountExpectedToProceedsMember" xlink:href="bxsl-20260930.xsd#bxsl_MeasurementInputDiscountExpectedToProceedsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MeasurementInputDiscountExpectedToProceedsMember" xlink:to="lab_bxsl_MeasurementInputDiscountExpectedToProceedsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MediaSectorMember_019fd71c-09ae-7e69-9e20-27697cfaf7bb_terseLabel_en-US" xlink:label="lab_bxsl_MediaSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Media</link:label>
    <link:label id="lab_bxsl_MediaSectorMember_label_en-US" xlink:label="lab_bxsl_MediaSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Media Sector [Member]</link:label>
    <link:label id="lab_bxsl_MediaSectorMember_documentation_en-US" xlink:label="lab_bxsl_MediaSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Media Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MediaSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_MediaSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MediaSectorMember" xlink:to="lab_bxsl_MediaSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019fd71c-09ae-7990-a630-ae6d9c2297a3_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityClassOfTreasuryStockLineItems_019fd71c-091c-7bcd-9ef4-d3a1b7ee8707_terseLabel_en-US" xlink:label="lab_us-gaap_EquityClassOfTreasuryStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity, Class of Treasury Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_EquityClassOfTreasuryStockLineItems_label_en-US" xlink:label="lab_us-gaap_EquityClassOfTreasuryStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Class of Treasury Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityClassOfTreasuryStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityClassOfTreasuryStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityClassOfTreasuryStockLineItems" xlink:to="lab_us-gaap_EquityClassOfTreasuryStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019fd71c-09ae-7d52-a32b-9fadcf811753_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentOwnedAtFairValueMember_019fd71c-09ae-76cd-976b-5f4f7bd3f4f4_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentOwnedAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Owned, At Fair Value</link:label>
    <link:label id="lab_bxsl_InvestmentOwnedAtFairValueMember_label_en-US" xlink:label="lab_bxsl_InvestmentOwnedAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, At Fair Value [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentOwnedAtFairValueMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentOwnedAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Owned, At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentOwnedAtFairValueMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentOwnedAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentOwnedAtFairValueMember" xlink:to="lab_bxsl_InvestmentOwnedAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityFee_019fd71c-09ae-7506-af94-48dac449b4a7_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityFee" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Facility unused fees</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityFee_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unused Borrowing Capacity, Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnusedBorrowingCapacityFee" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentUnusedBorrowingCapacityFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnusedBorrowingCapacityFee" xlink:to="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityFee" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019fd71c-09af-71cd-8918-77e7b03143d2_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributable earnings (loss)</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPayableForInvestmentPurchased_019fd71c-091c-7677-ba29-7e5c276a518e_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPayableForInvestmentPurchased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payable for investments</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPayableForInvestmentPurchased_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPayableForInvestmentPurchased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Payable for Investment Purchased</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPayableForInvestmentPurchased" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPayableForInvestmentPurchased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPayableForInvestmentPurchased" xlink:to="lab_us-gaap_IncreaseDecreaseInPayableForInvestmentPurchased" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingAfterTax_019fd71c-09af-777e-84aa-9a0729c68e65_terseLabel_en-US" xlink:label="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized gain (loss)</link:label>
    <link:label id="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingAfterTax_label_en-US" xlink:label="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Investment and Derivative, Operating, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingAfterTax" xlink:to="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive_019fd71c-09af-749b-b0f2-ac910092065d_terseLabel_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3 - 5 Years</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive_label_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term Maturities, Repayments of Principal in Rolling Year Three Through Five</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive_documentation_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term Maturities, Repayments of Principal in Rolling Year Three Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive" xlink:href="bxsl-20260930.xsd#bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive" xlink:to="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearThreeThroughFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019fd71c-09ae-7c31-bd01-fcda469a918b_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Par Amount</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MarineTransportationSectorMember_019fd71c-09ae-7306-bfe2-a664761b5134_terseLabel_en-US" xlink:label="lab_bxsl_MarineTransportationSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marine Transportation</link:label>
    <link:label id="lab_bxsl_MarineTransportationSectorMember_label_en-US" xlink:label="lab_bxsl_MarineTransportationSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marine Transportation Sector [Member]</link:label>
    <link:label id="lab_bxsl_MarineTransportationSectorMember_documentation_en-US" xlink:label="lab_bxsl_MarineTransportationSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marine Transportation Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MarineTransportationSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_MarineTransportationSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MarineTransportationSectorMember" xlink:to="lab_bxsl_MarineTransportationSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_Scenario1Member_019fd71c-09af-7af3-9d17-e27deb7e0ca2_terseLabel_en-US" xlink:label="lab_bxsl_Scenario1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario 1</link:label>
    <link:label id="lab_bxsl_Scenario1Member_label_en-US" xlink:label="lab_bxsl_Scenario1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario 1 [Member]</link:label>
    <link:label id="lab_bxsl_Scenario1Member_documentation_en-US" xlink:label="lab_bxsl_Scenario1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Scenario 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_Scenario1Member" xlink:href="bxsl-20260930.xsd#bxsl_Scenario1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_Scenario1Member" xlink:to="lab_bxsl_Scenario1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract_019fd71c-09af-7ed0-9bbd-a9cc8986f999_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ratios:</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract_label_en-US" xlink:label="lab_bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Ratio To Average Net Assets [Abstract]</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract_documentation_en-US" xlink:label="lab_bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Ratio To Average Net Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:to="lab_bxsl_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019fd71c-0a16-7fa7-a41d-3c6293acebcd_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_019fd71c-09ae-7ce4-85e4-8458f6c5541f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLC2Member_019fd71c-09af-7796-87e6-ede594cce0a1_terseLabel_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLC2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLC2Member_label_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLC2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC 2 [Member]</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLC2Member_documentation_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLC2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AlignPrecisionGroupLLC2Member" xlink:href="bxsl-20260930.xsd#bxsl_AlignPrecisionGroupLLC2Member"/>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019fd71c-09af-7b04-bc5b-969d4d375ebb_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and net assets</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_019fd71c-09af-767b-9f50-dd68c78e360d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases of investments</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_TechnologyHardwareStorageAndPeripheralsMember_019fd71c-0a16-7dd4-933e-e070824eb2d6_terseLabel_en-US" xlink:label="lab_bxsl_TechnologyHardwareStorageAndPeripheralsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Technology Hardware, Storage &amp; Peripherals</link:label>
    <link:label id="lab_bxsl_TechnologyHardwareStorageAndPeripheralsMember_label_en-US" xlink:label="lab_bxsl_TechnologyHardwareStorageAndPeripheralsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Technology Hardware, Storage and Peripherals [Member]</link:label>
    <link:label id="lab_bxsl_TechnologyHardwareStorageAndPeripheralsMember_documentation_en-US" xlink:label="lab_bxsl_TechnologyHardwareStorageAndPeripheralsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Technology Hardware, Storage and Peripherals</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_TechnologyHardwareStorageAndPeripheralsMember" xlink:href="bxsl-20260930.xsd#bxsl_TechnologyHardwareStorageAndPeripheralsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_TechnologyHardwareStorageAndPeripheralsMember" xlink:to="lab_bxsl_TechnologyHardwareStorageAndPeripheralsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncentiveFeePayableIncomeBased_019fd71c-09af-7195-b2b4-3bc9526a15f3_terseLabel_en-US" xlink:label="lab_us-gaap_IncentiveFeePayableIncomeBased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income based incentive fees payable (Note 3)</link:label>
    <link:label id="lab_us-gaap_IncentiveFeePayableIncomeBased_label_en-US" xlink:label="lab_us-gaap_IncentiveFeePayableIncomeBased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incentive Fee Payable, Income-Based</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncentiveFeePayableIncomeBased" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncentiveFeePayableIncomeBased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncentiveFeePayableIncomeBased" xlink:to="lab_us-gaap_IncentiveFeePayableIncomeBased" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_019fd71c-091c-7837-a21d-5b59f3601b90_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByAssetClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByAssetClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByAssetClassAxis" xlink:to="lab_us-gaap_FairValueByAssetClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019fd71c-09af-76a7-9267-702dc4b0b55a_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_Scenario2Member_019fd71c-091c-791f-b3a6-f8fa321fa8e0_terseLabel_en-US" xlink:label="lab_bxsl_Scenario2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario 2</link:label>
    <link:label id="lab_bxsl_Scenario2Member_label_en-US" xlink:label="lab_bxsl_Scenario2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario 2 [Member]</link:label>
    <link:label id="lab_bxsl_Scenario2Member_documentation_en-US" xlink:label="lab_bxsl_Scenario2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Scenario 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_Scenario2Member" xlink:href="bxsl-20260930.xsd#bxsl_Scenario2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_Scenario2Member" xlink:to="lab_bxsl_Scenario2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019fd71c-09af-7e6c-9515-25fcace9bd9a_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InterestPayableInterestExpense_019fd71c-0a16-7d05-8645-08f54308c6d5_terseLabel_en-US" xlink:label="lab_bxsl_InterestPayableInterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_bxsl_InterestPayableInterestExpense_label_en-US" xlink:label="lab_bxsl_InterestPayableInterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Interest Expense</link:label>
    <link:label id="lab_bxsl_InterestPayableInterestExpense_documentation_en-US" xlink:label="lab_bxsl_InterestPayableInterestExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Payable, Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InterestPayableInterestExpense" xlink:href="bxsl-20260930.xsd#bxsl_InterestPayableInterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InterestPayableInterestExpense" xlink:to="lab_bxsl_InterestPayableInterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIdentifierAxis_019fd71c-091c-7182-b00f-ba15144ce36d_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIdentifierAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Identifier [Axis]</link:label>
    <link:label id="lab_us-gaap_InvestmentIdentifierAxis_label_en-US" xlink:label="lab_us-gaap_InvestmentIdentifierAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Identifier [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIdentifierAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIdentifierAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIdentifierAxis" xlink:to="lab_us-gaap_InvestmentIdentifierAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtSecuritiesFirstLienMember_019fd71c-09af-7033-8760-19f2f73eb97d_terseLabel_en-US" xlink:label="lab_bxsl_DebtSecuritiesFirstLienMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">First lien debt</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesFirstLienMember_label_en-US" xlink:label="lab_bxsl_DebtSecuritiesFirstLienMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, First Lien [Member]</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesFirstLienMember_documentation_en-US" xlink:label="lab_bxsl_DebtSecuritiesFirstLienMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, First Lien</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtSecuritiesFirstLienMember" xlink:href="bxsl-20260930.xsd#bxsl_DebtSecuritiesFirstLienMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtSecuritiesFirstLienMember" xlink:to="lab_bxsl_DebtSecuritiesFirstLienMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketApproachValuationTechniqueMember_019fd71c-09ae-7681-8bbb-3c6f77f43409_terseLabel_en-US" xlink:label="lab_us-gaap_MarketApproachValuationTechniqueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Market Approach</link:label>
    <link:label id="lab_us-gaap_MarketApproachValuationTechniqueMember_label_en-US" xlink:label="lab_us-gaap_MarketApproachValuationTechniqueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation, Market Approach [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketApproachValuationTechniqueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MarketApproachValuationTechniqueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketApproachValuationTechniqueMember" xlink:to="lab_us-gaap_MarketApproachValuationTechniqueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_019fd71c-09af-7eb9-8fd0-200d979c1a74_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offering price per share (in usd per share)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_label_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockPricePerShare" xlink:to="lab_us-gaap_SaleOfStockPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_019fd71c-09af-7300-aa13-d2137e7349ff_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DelayedDrawTermLoansAndRevolversMember_019fd71c-09ae-71f6-aa39-44dd00b23542_terseLabel_en-US" xlink:label="lab_bxsl_DelayedDrawTermLoansAndRevolversMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Delayed Draw Term Loans And Revolvers</link:label>
    <link:label id="lab_bxsl_DelayedDrawTermLoansAndRevolversMember_label_en-US" xlink:label="lab_bxsl_DelayedDrawTermLoansAndRevolversMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Delayed Draw Term Loans And Revolvers [Member]</link:label>
    <link:label id="lab_bxsl_DelayedDrawTermLoansAndRevolversMember_documentation_en-US" xlink:label="lab_bxsl_DelayedDrawTermLoansAndRevolversMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Delayed Draw Term Loans And Revolvers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DelayedDrawTermLoansAndRevolversMember" xlink:href="bxsl-20260930.xsd#bxsl_DelayedDrawTermLoansAndRevolversMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DelayedDrawTermLoansAndRevolversMember" xlink:to="lab_bxsl_DelayedDrawTermLoansAndRevolversMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_Scenario3Member_019fd71c-09ae-714d-b5c8-91ef8aa64386_terseLabel_en-US" xlink:label="lab_bxsl_Scenario3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario 3</link:label>
    <link:label id="lab_bxsl_Scenario3Member_label_en-US" xlink:label="lab_bxsl_Scenario3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario 3 [Member]</link:label>
    <link:label id="lab_bxsl_Scenario3Member_documentation_en-US" xlink:label="lab_bxsl_Scenario3Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Scenario 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_Scenario3Member" xlink:href="bxsl-20260930.xsd#bxsl_Scenario3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_Scenario3Member" xlink:to="lab_bxsl_Scenario3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_RealizedGainLossDerivativeOperatingAfterTax_019fd71c-09af-7d9d-8aed-8322208fd158_terseLabel_en-US" xlink:label="lab_bxsl_RealizedGainLossDerivativeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments (Note 6)</link:label>
    <link:label id="lab_bxsl_RealizedGainLossDerivativeOperatingAfterTax_label_en-US" xlink:label="lab_bxsl_RealizedGainLossDerivativeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Derivative, Operating, After Tax</link:label>
    <link:label id="lab_bxsl_RealizedGainLossDerivativeOperatingAfterTax_documentation_en-US" xlink:label="lab_bxsl_RealizedGainLossDerivativeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Derivative, Operating, After Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_RealizedGainLossDerivativeOperatingAfterTax" xlink:href="bxsl-20260930.xsd#bxsl_RealizedGainLossDerivativeOperatingAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_RealizedGainLossDerivativeOperatingAfterTax" xlink:to="lab_bxsl_RealizedGainLossDerivativeOperatingAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInBrokerageReceivables_019fd71c-09af-7a14-a0ce-6b8c999051f1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInBrokerageReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Receivable from broker</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInBrokerageReceivables_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInBrokerageReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Receivable from Broker-Dealer and Clearing Organization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInBrokerageReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInBrokerageReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInBrokerageReceivables" xlink:to="lab_us-gaap_IncreaseDecreaseInBrokerageReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ITServicesSectorMember_019fd71c-09af-7c83-9ae4-ce754127e9ba_terseLabel_en-US" xlink:label="lab_bxsl_ITServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">IT Services</link:label>
    <link:label id="lab_bxsl_ITServicesSectorMember_label_en-US" xlink:label="lab_bxsl_ITServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">IT Services Sector [Member]</link:label>
    <link:label id="lab_bxsl_ITServicesSectorMember_documentation_en-US" xlink:label="lab_bxsl_ITServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">IT Services Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ITServicesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_ITServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ITServicesSectorMember" xlink:to="lab_bxsl_ITServicesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_BiotechnologySectorMember_019fd71c-09af-7bd3-b8cc-daaeaa8a5242_terseLabel_en-US" xlink:label="lab_bxsl_BiotechnologySectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Biotechnology</link:label>
    <link:label id="lab_bxsl_BiotechnologySectorMember_label_en-US" xlink:label="lab_bxsl_BiotechnologySectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Biotechnology Sector [Member]</link:label>
    <link:label id="lab_bxsl_BiotechnologySectorMember_documentation_en-US" xlink:label="lab_bxsl_BiotechnologySectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Biotechnology Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_BiotechnologySectorMember" xlink:href="bxsl-20260930.xsd#bxsl_BiotechnologySectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_BiotechnologySectorMember" xlink:to="lab_bxsl_BiotechnologySectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019fd71c-09ae-75e1-8266-5bdb1bf925c1_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid during the period</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_019fd71c-09ae-7ae1-a32f-b394c4c0529a_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for interest expense</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_019fd71c-09af-74df-821a-f42a8b327b54_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgingDesignationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationAxis" xlink:to="lab_us-gaap_HedgingDesignationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_019fd71c-0a16-7ae9-a020-3afb254ae60b_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_HealthCareEquipmentSuppliesSectorMember_019fd71c-091c-74c9-a108-041263109da7_terseLabel_en-US" xlink:label="lab_bxsl_HealthCareEquipmentSuppliesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Health Care Equipment &amp; Supplies</link:label>
    <link:label id="lab_bxsl_HealthCareEquipmentSuppliesSectorMember_label_en-US" xlink:label="lab_bxsl_HealthCareEquipmentSuppliesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Health Care Equipment &amp; Supplies Sector [Member]</link:label>
    <link:label id="lab_bxsl_HealthCareEquipmentSuppliesSectorMember_documentation_en-US" xlink:label="lab_bxsl_HealthCareEquipmentSuppliesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Health Care Equipment &amp; Supplies Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_HealthCareEquipmentSuppliesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_HealthCareEquipmentSuppliesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_HealthCareEquipmentSuppliesSectorMember" xlink:to="lab_bxsl_HealthCareEquipmentSuppliesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019fd71c-09ae-742b-a3d1-3074719995cf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019fd71c-09af-700d-8fad-4b733d17fd83_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019fd71c-091c-78e5-a8b3-b1cd0b397666_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InsuranceSectorMember_019fd71c-09af-7ed6-990b-9a0314dc7d00_terseLabel_en-US" xlink:label="lab_us-gaap_InsuranceSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance</link:label>
    <link:label id="lab_us-gaap_InsuranceSectorMember_label_en-US" xlink:label="lab_us-gaap_InsuranceSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Sector [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuranceSectorMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InsuranceSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InsuranceSectorMember" xlink:to="lab_us-gaap_InsuranceSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_LifeSciencesToolsServicesSectorMember_019fd71c-091c-7c8e-bcef-25a29284378a_terseLabel_en-US" xlink:label="lab_bxsl_LifeSciencesToolsServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Life Sciences Tools &amp; Services</link:label>
    <link:label id="lab_bxsl_LifeSciencesToolsServicesSectorMember_label_en-US" xlink:label="lab_bxsl_LifeSciencesToolsServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Life Sciences Tools &amp; Services Sector [Member]</link:label>
    <link:label id="lab_bxsl_LifeSciencesToolsServicesSectorMember_documentation_en-US" xlink:label="lab_bxsl_LifeSciencesToolsServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Life Sciences Tools &amp; Services Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_LifeSciencesToolsServicesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_LifeSciencesToolsServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_LifeSciencesToolsServicesSectorMember" xlink:to="lab_bxsl_LifeSciencesToolsServicesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_Scenario6Member_019fd71c-09af-7648-a67c-b27cef66927e_terseLabel_en-US" xlink:label="lab_bxsl_Scenario6Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario 6</link:label>
    <link:label id="lab_bxsl_Scenario6Member_label_en-US" xlink:label="lab_bxsl_Scenario6Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario 6 [Member]</link:label>
    <link:label id="lab_bxsl_Scenario6Member_documentation_en-US" xlink:label="lab_bxsl_Scenario6Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Scenario 6</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_Scenario6Member" xlink:href="bxsl-20260930.xsd#bxsl_Scenario6Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_Scenario6Member" xlink:to="lab_bxsl_Scenario6Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019fd71c-09ae-7186-b681-727883696791_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019fd71c-09ae-7e2b-b082-5ea15799a966_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction_019fd71c-09ae-7524-a0ea-458f4d193cd6_terseLabel_en-US" xlink:label="lab_us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued but unpaid debt issuance costs</link:label>
    <link:label id="lab_us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction_label_en-US" xlink:label="lab_us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs Incurred During Noncash or Partial Noncash Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction" xlink:to="lab_us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A2125SeniorNotesDue2027Member_019fd71c-091c-7a9f-9914-668667a3d2c6_terseLabel_en-US" xlink:label="lab_bxsl_A2125SeniorNotesDue2027Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2.125% Senior Notes Due 2027</link:label>
    <link:label id="lab_bxsl_A2125SeniorNotesDue2027Member_label_en-US" xlink:label="lab_bxsl_A2125SeniorNotesDue2027Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2.125% Senior Notes Due 2027 [Member]</link:label>
    <link:label id="lab_bxsl_A2125SeniorNotesDue2027Member_documentation_en-US" xlink:label="lab_bxsl_A2125SeniorNotesDue2027Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2.125% Senior Notes Due 2027</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A2125SeniorNotesDue2027Member" xlink:href="bxsl-20260930.xsd#bxsl_A2125SeniorNotesDue2027Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A2125SeniorNotesDue2027Member" xlink:to="lab_bxsl_A2125SeniorNotesDue2027Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredOvernightFinancingRateSofrMember_019fd71c-09af-759e-a5c7-27488fc4a71b_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SOFR</link:label>
    <link:label id="lab_us-gaap_SecuredOvernightFinancingRateSofrMember_label_en-US" xlink:label="lab_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Overnight Financing Rate (SOFR) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredOvernightFinancingRateSofrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:to="lab_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_Scenario5Member_019fd71c-091c-7565-b71f-b980006d9214_terseLabel_en-US" xlink:label="lab_bxsl_Scenario5Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario 5</link:label>
    <link:label id="lab_bxsl_Scenario5Member_label_en-US" xlink:label="lab_bxsl_Scenario5Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario 5 [Member]</link:label>
    <link:label id="lab_bxsl_Scenario5Member_documentation_en-US" xlink:label="lab_bxsl_Scenario5Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Scenario 5</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_Scenario5Member" xlink:href="bxsl-20260930.xsd#bxsl_Scenario5Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_Scenario5Member" xlink:to="lab_bxsl_Scenario5Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockLineItems_019fd71c-09af-72f0-9555-df5bcf8c68ea_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary, Sale of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Sale of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="lab_us-gaap_SubsidiarySaleOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeOperatingTaxExpenseBenefit_019fd71c-09af-7ecb-803e-4e02b7aefbca_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeOperatingTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excise and other tax expense</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeOperatingTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeOperatingTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Operating, Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeOperatingTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeOperatingTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeOperatingTaxExpenseBenefit" xlink:to="lab_us-gaap_InvestmentIncomeOperatingTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember_019fd71c-091c-7643-909e-de0801a91060_terseLabel_en-US" xlink:label="lab_bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Blackstone Donegal Holdings LP - LP Interests (Westland Insurance Group LTD)</link:label>
    <link:label id="lab_bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember_label_en-US" xlink:label="lab_bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Blackstone Donegal Holdings LP - LP Interests (Westland Insurance Group LTD) [Member]</link:label>
    <link:label id="lab_bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember_documentation_en-US" xlink:label="lab_bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Blackstone Donegal Holdings LP - LP Interests (Westland Insurance Group LTD)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember" xlink:href="bxsl-20260930.xsd#bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember" xlink:to="lab_bxsl_BlackstoneDonegalHoldingsLPLPInterestsWestlandInsuranceGroupLTDMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember_01a186f3-504a-7b14-b7b4-231850c018de_terseLabel_en-US" xlink:label="lab_bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Medallia, Inc. - Equity and other - Common Equity Class A</link:label>
    <link:label id="lab_bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember_label_en-US" xlink:label="lab_bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Medallia, Inc. - Equity and other - Common Equity Class A [Member]</link:label>
    <link:label id="lab_bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember_documentation_en-US" xlink:label="lab_bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Medallia, Inc. - Equity and other - Common Equity Class A</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember" xlink:href="bxsl-20260930.xsd#bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember" xlink:to="lab_bxsl_MedalliaInc.EquityAndOtherCommonEquityClassAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_PaidInKindInterestNoncash_019fd71c-09af-714f-8093-77797c53a256_negatedTerseLabel_en-US" xlink:label="lab_bxsl_PaidInKindInterestNoncash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment-in-kind interest capitalized</link:label>
    <link:label id="lab_bxsl_PaidInKindInterestNoncash_label_en-US" xlink:label="lab_bxsl_PaidInKindInterestNoncash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Paid In Kind Interest, Noncash</link:label>
    <link:label id="lab_bxsl_PaidInKindInterestNoncash_documentation_en-US" xlink:label="lab_bxsl_PaidInKindInterestNoncash" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Paid In Kind Interest, Noncash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_PaidInKindInterestNoncash" xlink:href="bxsl-20260930.xsd#bxsl_PaidInKindInterestNoncash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_PaidInKindInterestNoncash" xlink:to="lab_bxsl_PaidInKindInterestNoncash" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityNotionalAmount_019fd71c-09ae-731e-9940-353ca315f27a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityNotionalAmount" xlink:to="lab_us-gaap_DerivativeLiabilityNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019fd71c-09ae-7d8b-8a1f-35c88b1015d2_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in net assets resulting from operations</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019fd71c-09ae-7311-932c-a368468da07a_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in net assets resulting from operations</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019fd71c-0a16-79c7-bd20-dfd6c193ac77_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsMember_019fd71c-09ae-763b-a0f0-0513f99ca6b5_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_InvestmentsMember_label_en-US" xlink:label="lab_us-gaap_InvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsMember" xlink:to="lab_us-gaap_InvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_Scenario4Member_019fd71c-0a16-7549-a580-d37448297c4b_terseLabel_en-US" xlink:label="lab_bxsl_Scenario4Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario 4</link:label>
    <link:label id="lab_bxsl_Scenario4Member_label_en-US" xlink:label="lab_bxsl_Scenario4Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario 4 [Member]</link:label>
    <link:label id="lab_bxsl_Scenario4Member_documentation_en-US" xlink:label="lab_bxsl_Scenario4Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Scenario 4</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_Scenario4Member" xlink:href="bxsl-20260930.xsd#bxsl_Scenario4Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_Scenario4Member" xlink:to="lab_bxsl_Scenario4Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDerivativeAssets_019fd71c-09af-76ab-82c4-034cb352c536_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDerivativeAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDerivativeAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Derivative Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInDerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDerivativeAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInDerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A5.875NotesDue2027Member_019fd71c-0a16-767c-a123-9a3a6b5f28e7_terseLabel_en-US" xlink:label="lab_bxsl_A5.875NotesDue2027Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.875% Notes Due 2027</link:label>
    <link:label id="lab_bxsl_A5.875NotesDue2027Member_label_en-US" xlink:label="lab_bxsl_A5.875NotesDue2027Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5.875% Notes Due 2027 [Member]</link:label>
    <link:label id="lab_bxsl_A5.875NotesDue2027Member_documentation_en-US" xlink:label="lab_bxsl_A5.875NotesDue2027Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5.875% Notes Due 2027</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A5.875NotesDue2027Member" xlink:href="bxsl-20260930.xsd#bxsl_A5.875NotesDue2027Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A5.875NotesDue2027Member" xlink:to="lab_bxsl_A5.875NotesDue2027Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_019fd71c-09af-7f8d-a047-44e38d7147b8_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment income:</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtInstrumentFloorInterestRate_019fd71c-0a16-7a1c-a869-06b3a39e0321_terseLabel_en-US" xlink:label="lab_bxsl_DebtInstrumentFloorInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate floor percentage</link:label>
    <link:label id="lab_bxsl_DebtInstrumentFloorInterestRate_label_en-US" xlink:label="lab_bxsl_DebtInstrumentFloorInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Floor Interest Rate</link:label>
    <link:label id="lab_bxsl_DebtInstrumentFloorInterestRate_documentation_en-US" xlink:label="lab_bxsl_DebtInstrumentFloorInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Floor Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtInstrumentFloorInterestRate" xlink:href="bxsl-20260930.xsd#bxsl_DebtInstrumentFloorInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtInstrumentFloorInterestRate" xlink:to="lab_bxsl_DebtInstrumentFloorInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019fd71c-091c-7423-acc8-1b0974ea10db_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019fd71c-091c-7afa-b2ed-d9814a54fcdc_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_019fd71c-09af-7903-8c1d-a0f43a735424_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives Available for Offset</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Asset Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityFairValueGrossAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:to="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityCollateralRightToReclaimCashOffset_019fd71c-091c-7db8-bb5f-1e1314c75cdf_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityCollateralRightToReclaimCashOffset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral Offset</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityCollateralRightToReclaimCashOffset_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityCollateralRightToReclaimCashOffset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Cash Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityCollateralRightToReclaimCashOffset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityCollateralRightToReclaimCashOffset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityCollateralRightToReclaimCashOffset" xlink:to="lab_us-gaap_DerivativeLiabilityCollateralRightToReclaimCashOffset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueOptionPricingModelMember_019fd71c-09ae-7676-b6ef-d9b8e1556c07_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Option Pricing Model</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueOptionPricingModelMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Option Pricing Model [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueOptionPricingModelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:to="lab_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ManagementAndServiceFeesIncomeBasedIncentiveRateCatchUpPercentage_019fd71c-09ae-7b22-85f8-073748c13656_terseLabel_en-US" xlink:label="lab_bxsl_ManagementAndServiceFeesIncomeBasedIncentiveRateCatchUpPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Incentive rate, catch up, percentage</link:label>
    <link:label id="lab_bxsl_ManagementAndServiceFeesIncomeBasedIncentiveRateCatchUpPercentage_label_en-US" xlink:label="lab_bxsl_ManagementAndServiceFeesIncomeBasedIncentiveRateCatchUpPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management And Service Fees, Income Based Incentive Rate, Catch up, Percentage</link:label>
    <link:label id="lab_bxsl_ManagementAndServiceFeesIncomeBasedIncentiveRateCatchUpPercentage_documentation_en-US" xlink:label="lab_bxsl_ManagementAndServiceFeesIncomeBasedIncentiveRateCatchUpPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management And Service Fees, Income Based Incentive Rate, Catch up, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ManagementAndServiceFeesIncomeBasedIncentiveRateCatchUpPercentage" xlink:href="bxsl-20260930.xsd#bxsl_ManagementAndServiceFeesIncomeBasedIncentiveRateCatchUpPercentage"/>
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    <link:label id="lab_us-gaap_CommonStockValue_019fd71c-0a16-7949-8f5b-95bbced5a00d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Shares, $0.001 par value (unlimited shares authorized; 232,970,063 and 231,969,058 shares issued and outstanding, respectively)</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpense_019fd71c-09ae-7818-a50e-1a99b6952f58_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpense_019fd71c-09ae-7749-a57c-4ecc7cdaeeef_totalLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpense_label_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating and Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpense" xlink:to="lab_us-gaap_InterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_019fd71c-09ae-7abc-9355-35ef64a42327_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear_019fd71c-0a16-78fa-b61a-1106425e5178_terseLabel_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 1 Year</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear_label_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term Maturities, Repayments of Principal in Rolling Less Than One Year</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear_documentation_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term Maturities, Repayments of Principal in Rolling Less Than One Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear" xlink:href="bxsl-20260930.xsd#bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear" xlink:to="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingLessThanOneYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_019fd71c-0a16-7b27-a6d6-8a9e1b6675ef_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDeterminationDate"/>
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    <link:label id="lab_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset_019fd71c-09af-7ccc-9a34-61496916a6c1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral Offset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Cash, Offset Against Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset"/>
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    <link:label id="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit_019fd71c-09ae-7440-9ab5-ae44ae52436c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current tax expense on realized gains</link:label>
    <link:label id="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Investment and Derivative, Operating, Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:to="lab_us-gaap_RealizedGainLossInvestmentAndDerivativeOperatingTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentUnaffiliatedIssuerMember_019fd71c-09ae-7988-baca-ca7f43795d90_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentUnaffiliatedIssuerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-controlled/non-affiliated investments</link:label>
    <link:label id="lab_us-gaap_InvestmentUnaffiliatedIssuerMember_label_en-US" xlink:label="lab_us-gaap_InvestmentUnaffiliatedIssuerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Unaffiliated Issuer [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentUnaffiliatedIssuerMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentUnaffiliatedIssuerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentUnaffiliatedIssuerMember" xlink:to="lab_us-gaap_InvestmentUnaffiliatedIssuerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019fd71c-0a16-7e9a-ae31-5387e0c8531b_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetInvestmentIncome_019fd71c-09ae-7368-ae47-9b74d2008f8a_totalLabel_en-US" xlink:label="lab_us-gaap_NetInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net investment income before tax expense</link:label>
    <link:label id="lab_us-gaap_NetInvestmentIncome_label_en-US" xlink:label="lab_us-gaap_NetInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Investment Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetInvestmentIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetInvestmentIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetInvestmentIncome" xlink:to="lab_us-gaap_NetInvestmentIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_VoluntaryWaiverScenarioDomain_019fd71c-09af-7c55-b237-a2dabe0d262e_terseLabel_en-US" xlink:label="lab_bxsl_VoluntaryWaiverScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Voluntary Waiver Scenario [Domain]</link:label>
    <link:label id="lab_bxsl_VoluntaryWaiverScenarioDomain_label_en-US" xlink:label="lab_bxsl_VoluntaryWaiverScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Voluntary Waiver Scenario [Domain]</link:label>
    <link:label id="lab_bxsl_VoluntaryWaiverScenarioDomain_documentation_en-US" xlink:label="lab_bxsl_VoluntaryWaiverScenarioDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Voluntary Waiver Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_VoluntaryWaiverScenarioDomain" xlink:href="bxsl-20260930.xsd#bxsl_VoluntaryWaiverScenarioDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_VoluntaryWaiverScenarioDomain" xlink:to="lab_bxsl_VoluntaryWaiverScenarioDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_UnsecuredNotesMember_019fd71c-09ae-78c4-8cb6-104cd38e990f_terseLabel_en-US" xlink:label="lab_bxsl_UnsecuredNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Notes</link:label>
    <link:label id="lab_bxsl_UnsecuredNotesMember_label_en-US" xlink:label="lab_bxsl_UnsecuredNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Notes [Member]</link:label>
    <link:label id="lab_bxsl_UnsecuredNotesMember_documentation_en-US" xlink:label="lab_bxsl_UnsecuredNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_UnsecuredNotesMember" xlink:href="bxsl-20260930.xsd#bxsl_UnsecuredNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_UnsecuredNotesMember" xlink:to="lab_bxsl_UnsecuredNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember_019fd71c-09ae-78fd-9288-f909e2596f4e_terseLabel_en-US" xlink:label="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CitiBank, Revolving Credit Facility, Revolving Commitments</link:label>
    <link:label id="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember_label_en-US" xlink:label="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CitiBank, Revolving Credit Facility, Revolving Commitments [Member]</link:label>
    <link:label id="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember_documentation_en-US" xlink:label="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CitiBank, Revolving Credit Facility, Revolving Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember" xlink:href="bxsl-20260930.xsd#bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember" xlink:to="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_019fd71c-09af-7523-982e-c49cd77ca7ed_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:to="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage_019fd71c-09af-775c-9900-8cfb37af2a40_terseLabel_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum utilization percentage</link:label>
    <link:label id="lab_bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage_label_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Minimum Capacity Utilization, Percentage</link:label>
    <link:label id="lab_bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage_documentation_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Minimum Capacity Utilization, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage" xlink:href="bxsl-20260930.xsd#bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage" xlink:to="lab_bxsl_LineOfCreditFacilityMinimumCapacityUtilizationPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentsUnrealizedGainLossMember_019fd71c-09af-7b69-bb9e-4964d66d3781_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentsUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_bxsl_InvestmentsUnrealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_InvestmentsUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Unrealized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentsUnrealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentsUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentsUnrealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentsUnrealizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentsUnrealizedGainLossMember" xlink:to="lab_bxsl_InvestmentsUnrealizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInManagementFeePayable_019fd71c-09af-796e-8601-bdffcc7dd446_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInManagementFeePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fees payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInManagementFeePayable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInManagementFeePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Management Fee Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInManagementFeePayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInManagementFeePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInManagementFeePayable" xlink:to="lab_us-gaap_IncreaseDecreaseInManagementFeePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A5.350NotesDue2028Member_019fd71c-091c-7e81-ac1a-f1499b7c7684_terseLabel_en-US" xlink:label="lab_bxsl_A5.350NotesDue2028Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.350% Notes Due 2028</link:label>
    <link:label id="lab_bxsl_A5.350NotesDue2028Member_label_en-US" xlink:label="lab_bxsl_A5.350NotesDue2028Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5.350% Notes Due 2028 [Member]</link:label>
    <link:label id="lab_bxsl_A5.350NotesDue2028Member_documentation_en-US" xlink:label="lab_bxsl_A5.350NotesDue2028Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5.350% Notes Due 2028</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A5.350NotesDue2028Member" xlink:href="bxsl-20260930.xsd#bxsl_A5.350NotesDue2028Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A5.350NotesDue2028Member" xlink:to="lab_bxsl_A5.350NotesDue2028Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount_019fd71c-09af-7af1-a2fb-f2331e3c60e1_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated future amount</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount_label_en-US" xlink:label="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Commitment to Investee, Estimated Future Amount</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount_documentation_en-US" xlink:label="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Commitment to Investee, Estimated Future Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount" xlink:to="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeEstimatedFutureAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_019fd71c-091c-7730-bdc9-a255d3dfc8f3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers into level 3</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Transfers Into Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019fd71c-09ae-7041-8383-c9e613fce139_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_EquitySecuritiesRealizedGainLossMember_019fd71c-091c-7e97-95e1-1a652ca0b2e8_terseLabel_en-US" xlink:label="lab_bxsl_EquitySecuritiesRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Securities, Realized Gain (Loss)</link:label>
    <link:label id="lab_bxsl_EquitySecuritiesRealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_EquitySecuritiesRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, Realized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_EquitySecuritiesRealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_EquitySecuritiesRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_EquitySecuritiesRealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_EquitySecuritiesRealizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_EquitySecuritiesRealizedGainLossMember" xlink:to="lab_bxsl_EquitySecuritiesRealizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueNetAbstract_019fd71c-09af-7816-bc66-092f907dc033_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueNetAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset of Collateral [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityFairValueNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityFairValueNetAbstract" xlink:to="lab_us-gaap_DerivativeLiabilityFairValueNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019fd71c-09af-7573-a993-43f3f19bb8df_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ShareRepurchaseProgramDomain_019fd71c-09ae-7a5a-af2f-0d07101930e8_terseLabel_en-US" xlink:label="lab_srt_ShareRepurchaseProgramDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Domain]</link:label>
    <link:label id="lab_srt_ShareRepurchaseProgramDomain_label_en-US" xlink:label="lab_srt_ShareRepurchaseProgramDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ShareRepurchaseProgramDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ShareRepurchaseProgramDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ShareRepurchaseProgramDomain" xlink:to="lab_srt_ShareRepurchaseProgramDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019fd71c-09ae-76e8-bb79-f0c5dc962675_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermCombinedAmountGross_019fd71c-09af-7551-b173-5a31a23f38e0_totalLabel_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermCombinedAmountGross" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermCombinedAmountGross_label_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermCombinedAmountGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term, Combined Amount, Gross</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermCombinedAmountGross_documentation_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermCombinedAmountGross" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term, Combined Amount, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtLongTermAndShortTermCombinedAmountGross" xlink:href="bxsl-20260930.xsd#bxsl_DebtLongTermAndShortTermCombinedAmountGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtLongTermAndShortTermCombinedAmountGross" xlink:to="lab_bxsl_DebtLongTermAndShortTermCombinedAmountGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_019fd71c-09af-717f-b726-a429114edac1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsAbstract_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInvestmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsAbstract" xlink:to="lab_us-gaap_ScheduleOfInvestmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A20241CLODebtMember_019fd71c-09af-7dad-9e5f-023594b979e8_terseLabel_en-US" xlink:label="lab_bxsl_A20241CLODebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024-1 CLO Debt</link:label>
    <link:label id="lab_bxsl_A20241CLODebtMember_label_en-US" xlink:label="lab_bxsl_A20241CLODebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024-1 CLO Debt [Member]</link:label>
    <link:label id="lab_bxsl_A20241CLODebtMember_documentation_en-US" xlink:label="lab_bxsl_A20241CLODebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024-1 CLO Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A20241CLODebtMember" xlink:href="bxsl-20260930.xsd#bxsl_A20241CLODebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A20241CLODebtMember" xlink:to="lab_bxsl_A20241CLODebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtAverageAmountOutstanding_019fd71c-09ae-79d2-ae0a-6469cbaed428_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAverageAmountOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average principal debt outstanding</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAverageAmountOutstanding_label_en-US" xlink:label="lab_us-gaap_LongTermDebtAverageAmountOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Average Amount Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtAverageAmountOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtAverageAmountOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtAverageAmountOutstanding" xlink:to="lab_us-gaap_LongTermDebtAverageAmountOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
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    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019fd71c-0a16-7be2-b62b-75f2ed81b53f_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit_019fd71c-09af-723a-aca6-019b12a0a920_terseLabel_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accordion feature</link:label>
    <link:label id="lab_bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit_label_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Accordion Feature, Increase Limit</link:label>
    <link:label id="lab_bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit_documentation_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Accordion Feature, Increase Limit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:href="bxsl-20260930.xsd#bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:to="lab_bxsl_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan_019fd71c-09ae-7ece-b86e-739840c4047a_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Reinvestment of dividends</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan_019fd71c-09ae-7d23-8e76-612cf3668ab8_netLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">DRIP Shares Value</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Dividend Reinvestment Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueDividendReinvestmentPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossReductions_019fd71c-091c-7889-a2ed-0d5c13ddb4cc_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossReductions" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gross Reductions</link:label>
    <link:label id="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossReductions_label_en-US" xlink:label="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossReductions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in and Advances to Affiliates, at Fair Value, Gross Reductions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossReductions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossReductions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossReductions" xlink:to="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossReductions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019fd71c-09af-70e1-9352-9105d20e4bbe_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit facility, maximum borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019fd71c-09af-7eca-a3b4-3f6d0d89aef2_verboseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Principal Committed</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyNetAssetValuePerSharePeriodIncreaseDecrease_019fd71c-09ae-769e-9e46-619dd25e039e_totalLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyNetAssetValuePerSharePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total increase (decrease) in net assets (in usd per share)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyNetAssetValuePerSharePeriodIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyNetAssetValuePerSharePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Net Asset Value, Per Share, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyNetAssetValuePerSharePeriodIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyNetAssetValuePerSharePeriodIncreaseDecrease"/>
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    <link:label id="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTextBlock_019fd71c-09ae-7d2a-be1f-5a8b31db54a1_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentHoldingsScheduleOfInvestmentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTextBlock" xlink:to="lab_us-gaap_InvestmentHoldingsScheduleOfInvestmentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_RelatedPartyTransactionRenewalTerm_019fd71c-09ae-7c4f-86bf-60a2effec6e2_terseLabel_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, renewal term</link:label>
    <link:label id="lab_bxsl_RelatedPartyTransactionRenewalTerm_label_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Renewal Term</link:label>
    <link:label id="lab_bxsl_RelatedPartyTransactionRenewalTerm_documentation_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Renewal Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_RelatedPartyTransactionRenewalTerm" xlink:href="bxsl-20260930.xsd#bxsl_RelatedPartyTransactionRenewalTerm"/>
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    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_019fd71c-09af-725c-8c0a-b5b0b8f44a97_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock by Subsidiary or Equity Investee [Table]</link:label>
    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_label_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock, Type [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_019fd71c-091c-70db-a341-e215b18b011a_totalLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total expenses before tax expense</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Investment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInvestmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:to="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019fd71c-09af-7169-b0b3-ee06789bdee0_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recent Accounting Pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019fd71c-09ae-7a8e-bba3-07d4334a3100_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of original issue discount and debt issuance costs (including premiums and discounts)</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnsecuredDebtMember_019fd71c-09ae-78cc-9b5d-dec59af18279_terseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured debt</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_UnsecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnsecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnsecuredDebtMember" xlink:to="lab_us-gaap_UnsecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan_019fd71c-09ae-7c67-940b-c3200268ecd4_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DRIP shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Dividend Reinvestment Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_019fd71c-0a16-70ed-9f68-39f0dcca0e9e_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt (net of unamortized debt issuance costs of $46,470 and $39,900, respectively)</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019fd71c-0a16-79af-a490-60f30ff399d6_netLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019fd71c-0a16-7f29-89f8-5900da7a5b61_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value (net of unamortized issuance costs, premiums and discounts)</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MaterialHoldingsLLCFirstLienDebt2Member_019fd71c-0a16-79bf-87d4-86aa7f96711b_terseLabel_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLCFirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC - First Lien Debt</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLCFirstLienDebt2Member_label_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLCFirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC - First Lien Debt 2 [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLCFirstLienDebt2Member_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLCFirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC - First Lien Debt 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingsLLCFirstLienDebt2Member" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingsLLCFirstLienDebt2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MaterialHoldingsLLCFirstLienDebt2Member" xlink:to="lab_bxsl_MaterialHoldingsLLCFirstLienDebt2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_NumberOfEquityDistributionAgreements_019fd71c-091c-7200-8da8-abb93efcddfb_terseLabel_en-US" xlink:label="lab_bxsl_NumberOfEquityDistributionAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of agreements</link:label>
    <link:label id="lab_bxsl_NumberOfEquityDistributionAgreements_label_en-US" xlink:label="lab_bxsl_NumberOfEquityDistributionAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Equity Distribution Agreements</link:label>
    <link:label id="lab_bxsl_NumberOfEquityDistributionAgreements_documentation_en-US" xlink:label="lab_bxsl_NumberOfEquityDistributionAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Equity Distribution Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_NumberOfEquityDistributionAgreements" xlink:href="bxsl-20260930.xsd#bxsl_NumberOfEquityDistributionAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_NumberOfEquityDistributionAgreements" xlink:to="lab_bxsl_NumberOfEquityDistributionAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_QualifyingAssetsMember_019fd71c-0a16-70bb-a4ff-e954d4bad12f_terseLabel_en-US" xlink:label="lab_bxsl_QualifyingAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Qualifying Assets</link:label>
    <link:label id="lab_bxsl_QualifyingAssetsMember_label_en-US" xlink:label="lab_bxsl_QualifyingAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Qualifying Assets [Member]</link:label>
    <link:label id="lab_bxsl_QualifyingAssetsMember_documentation_en-US" xlink:label="lab_bxsl_QualifyingAssetsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Qualifying Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_QualifyingAssetsMember" xlink:href="bxsl-20260930.xsd#bxsl_QualifyingAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_QualifyingAssetsMember" xlink:to="lab_bxsl_QualifyingAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A2750NotesDue2026Member_019fd71c-09af-7dac-aa0a-90c66bc32171_terseLabel_en-US" xlink:label="lab_bxsl_A2750NotesDue2026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2.750% Notes Due 2026</link:label>
    <link:label id="lab_bxsl_A2750NotesDue2026Member_label_en-US" xlink:label="lab_bxsl_A2750NotesDue2026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2.750% Notes Due 2026 [Member]</link:label>
    <link:label id="lab_bxsl_A2750NotesDue2026Member_documentation_en-US" xlink:label="lab_bxsl_A2750NotesDue2026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2.750% Notes Due 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A2750NotesDue2026Member" xlink:href="bxsl-20260930.xsd#bxsl_A2750NotesDue2026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A2750NotesDue2026Member" xlink:to="lab_bxsl_A2750NotesDue2026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_019fd71c-091c-7bd8-ac34-11c24e46ad9a_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_019fd71c-09af-7478-b58f-08eda4702170_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral Received Not Offset</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralObligationToReturnCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:to="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019fd71c-091c-72b1-bb92-e33b213e9222_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Assets</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019fd71c-09af-7705-a6a4-5e4280aa33ea_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019fd71c-09ae-79f3-8011-01f44df710d9_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_UnsecuredDebtRealizedGainLossMember_019fd71c-09af-7251-b68b-187a679aa27f_terseLabel_en-US" xlink:label="lab_bxsl_UnsecuredDebtRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Realized Gain (Loss)</link:label>
    <link:label id="lab_bxsl_UnsecuredDebtRealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_UnsecuredDebtRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Realized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_UnsecuredDebtRealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_UnsecuredDebtRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_UnsecuredDebtRealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_UnsecuredDebtRealizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_UnsecuredDebtRealizedGainLossMember" xlink:to="lab_bxsl_UnsecuredDebtRealizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_019fd71c-09ae-793f-aa53-bc03025d3ab9_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InterestRateSwap5Member_019fd71c-09ae-704a-9fdf-2e7b918fbf34_terseLabel_en-US" xlink:label="lab_bxsl_InterestRateSwap5Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 5</link:label>
    <link:label id="lab_bxsl_InterestRateSwap5Member_label_en-US" xlink:label="lab_bxsl_InterestRateSwap5Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 5 [Member]</link:label>
    <link:label id="lab_bxsl_InterestRateSwap5Member_documentation_en-US" xlink:label="lab_bxsl_InterestRateSwap5Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 5</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InterestRateSwap5Member" xlink:href="bxsl-20260930.xsd#bxsl_InterestRateSwap5Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InterestRateSwap5Member" xlink:to="lab_bxsl_InterestRateSwap5Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities_019fd71c-0a16-79e3-99c3-fac49c712130_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral Posted</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Security Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralRightToReclaimSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:to="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseBorrowings_019fd71c-09af-7e32-b4f5-fa191ea7618e_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowing interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseBorrowings_label_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Borrowings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseBorrowings" xlink:to="lab_us-gaap_InterestExpenseBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A5.125NotesDue2031Member_019fd71c-09af-7fd4-b6b0-80ad29f3d81f_terseLabel_en-US" xlink:label="lab_bxsl_A5.125NotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.125% Notes Due 2031</link:label>
    <link:label id="lab_bxsl_A5.125NotesDue2031Member_label_en-US" xlink:label="lab_bxsl_A5.125NotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5.125% Notes Due 2031 [Member]</link:label>
    <link:label id="lab_bxsl_A5.125NotesDue2031Member_documentation_en-US" xlink:label="lab_bxsl_A5.125NotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5.125% Notes Due 2031</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A5.125NotesDue2031Member" xlink:href="bxsl-20260930.xsd#bxsl_A5.125NotesDue2031Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A5.125NotesDue2031Member" xlink:to="lab_bxsl_A5.125NotesDue2031Member" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_019fd71c-09af-7331-8e8f-d1730fb3aba7_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_RealEstateManagementDevelopmentSectorMember_019fd71c-09af-7149-82fc-7de532210da9_terseLabel_en-US" xlink:label="lab_bxsl_RealEstateManagementDevelopmentSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Management &amp; Development</link:label>
    <link:label id="lab_bxsl_RealEstateManagementDevelopmentSectorMember_label_en-US" xlink:label="lab_bxsl_RealEstateManagementDevelopmentSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Management &amp; Development Sector [Member]</link:label>
    <link:label id="lab_bxsl_RealEstateManagementDevelopmentSectorMember_documentation_en-US" xlink:label="lab_bxsl_RealEstateManagementDevelopmentSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Management &amp; Development Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_RealEstateManagementDevelopmentSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_RealEstateManagementDevelopmentSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_RealEstateManagementDevelopmentSectorMember" xlink:to="lab_bxsl_RealEstateManagementDevelopmentSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_CitiBankRevolvingCreditFacilityMember_019fd71c-09ae-7a61-8b6e-6398ae48eb1e_terseLabel_en-US" xlink:label="lab_bxsl_CitiBankRevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility</link:label>
    <link:label id="lab_bxsl_CitiBankRevolvingCreditFacilityMember_label_en-US" xlink:label="lab_bxsl_CitiBankRevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CitiBank, Revolving Credit Facility [Member]</link:label>
    <link:label id="lab_bxsl_CitiBankRevolvingCreditFacilityMember_documentation_en-US" xlink:label="lab_bxsl_CitiBankRevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CitiBank, Revolving Credit Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_CitiBankRevolvingCreditFacilityMember" xlink:href="bxsl-20260930.xsd#bxsl_CitiBankRevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_CitiBankRevolvingCreditFacilityMember" xlink:to="lab_bxsl_CitiBankRevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtSecuritiesVariableRateMember_019fd71c-09af-7599-b841-88bc421632f6_terseLabel_en-US" xlink:label="lab_bxsl_DebtSecuritiesVariableRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Variable Rate</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesVariableRateMember_label_en-US" xlink:label="lab_bxsl_DebtSecuritiesVariableRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Variable Rate [Member]</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesVariableRateMember_documentation_en-US" xlink:label="lab_bxsl_DebtSecuritiesVariableRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtSecuritiesVariableRateMember" xlink:href="bxsl-20260930.xsd#bxsl_DebtSecuritiesVariableRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtSecuritiesVariableRateMember" xlink:to="lab_bxsl_DebtSecuritiesVariableRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_CommitmentFeeScenarioAxis_019fd71c-09ae-7bbe-830c-dd3e762837b5_terseLabel_en-US" xlink:label="lab_bxsl_CommitmentFeeScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitment Fee Scenario [Axis]</link:label>
    <link:label id="lab_bxsl_CommitmentFeeScenarioAxis_label_en-US" xlink:label="lab_bxsl_CommitmentFeeScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitment Fee Scenario [Axis]</link:label>
    <link:label id="lab_bxsl_CommitmentFeeScenarioAxis_documentation_en-US" xlink:label="lab_bxsl_CommitmentFeeScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commitment Fee Scenario</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_CommitmentFeeScenarioAxis" xlink:href="bxsl-20260930.xsd#bxsl_CommitmentFeeScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_CommitmentFeeScenarioAxis" xlink:to="lab_bxsl_CommitmentFeeScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsTable_019fd71c-09af-7225-b90e-461c787aab9f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentPortfolioMember_019fd71c-09af-7383-926c-0eae7af3a389_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentPortfolioMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Portfolio</link:label>
    <link:label id="lab_bxsl_InvestmentPortfolioMember_label_en-US" xlink:label="lab_bxsl_InvestmentPortfolioMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Portfolio [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentPortfolioMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentPortfolioMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Portfolio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentPortfolioMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentPortfolioMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentPortfolioMember" xlink:to="lab_bxsl_InvestmentPortfolioMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_019fd71c-0a16-7c1e-92c8-06d6a70dc2c5_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of original issue discount and debt issuance costs (including premiums and discounts)</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs and Discounts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCostsAndDiscounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:to="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentPortfolioCashAndCashEquivalentMember_019fd71c-09ae-7d39-b27b-bc2264f3971a_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentPortfolioCashAndCashEquivalentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Portfolio, Cash And Cash Equivalent</link:label>
    <link:label id="lab_bxsl_InvestmentPortfolioCashAndCashEquivalentMember_label_en-US" xlink:label="lab_bxsl_InvestmentPortfolioCashAndCashEquivalentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Portfolio, Cash And Cash Equivalent [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentPortfolioCashAndCashEquivalentMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentPortfolioCashAndCashEquivalentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Portfolio, Cash And Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentPortfolioCashAndCashEquivalentMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentPortfolioCashAndCashEquivalentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentPortfolioCashAndCashEquivalentMember" xlink:to="lab_bxsl_InvestmentPortfolioCashAndCashEquivalentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_JacksonHoleFundingFacilityMember_019fd71c-09af-77f3-9009-a7e1e5ab07fc_terseLabel_en-US" xlink:label="lab_bxsl_JacksonHoleFundingFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Jackson Hole Funding Facility</link:label>
    <link:label id="lab_bxsl_JacksonHoleFundingFacilityMember_label_en-US" xlink:label="lab_bxsl_JacksonHoleFundingFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Jackson Hole Funding Facility [Member]</link:label>
    <link:label id="lab_bxsl_JacksonHoleFundingFacilityMember_documentation_en-US" xlink:label="lab_bxsl_JacksonHoleFundingFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Jackson Hole Funding Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_JacksonHoleFundingFacilityMember" xlink:href="bxsl-20260930.xsd#bxsl_JacksonHoleFundingFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_JacksonHoleFundingFacilityMember" xlink:to="lab_bxsl_JacksonHoleFundingFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_019fd71c-09ae-7e5d-9998-1417f56f0399_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net change in unrealized (appreciation) depreciation on derivative instruments</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_019fd71c-09ae-70eb-9dd6-82f8e098d99d_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net change in unrealized appreciation (depreciation)</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossOnDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:to="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_Company10b18PlanMember_019fd71c-0a16-7b55-a363-9bc3ecdfa640_terseLabel_en-US" xlink:label="lab_bxsl_Company10b18PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company 10b-18 Plan</link:label>
    <link:label id="lab_bxsl_Company10b18PlanMember_label_en-US" xlink:label="lab_bxsl_Company10b18PlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company 10b-18 Plan [Member]</link:label>
    <link:label id="lab_bxsl_Company10b18PlanMember_documentation_en-US" xlink:label="lab_bxsl_Company10b18PlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Company 10b-18 Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_Company10b18PlanMember" xlink:href="bxsl-20260930.xsd#bxsl_Company10b18PlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_Company10b18PlanMember" xlink:to="lab_bxsl_Company10b18PlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019fd71c-091c-76b7-888e-8bf751298af7_netLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Principal outstanding</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019fd71c-091c-7655-9e7c-85e9b500f883_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Principal</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember_019fd71c-09af-7dd6-82da-63f4845bb1ef_terseLabel_en-US" xlink:label="lab_bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class C Notes, Mezzanine Secured Deferrable Floating Rate</link:label>
    <link:label id="lab_bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember_label_en-US" xlink:label="lab_bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class C Notes, Mezzanine Secured Deferrable Floating Rate [Member]</link:label>
    <link:label id="lab_bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember_documentation_en-US" xlink:label="lab_bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class C Notes, Mezzanine Secured Deferrable Floating Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember" xlink:href="bxsl-20260930.xsd#bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember" xlink:to="lab_bxsl_A20241CLOClassCNotesMezzanineSecuredDeferrableFloatingRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_SpecialtyRetailSectorMember_019fd71c-09af-75ab-a9dc-1d0d6cd7f86e_terseLabel_en-US" xlink:label="lab_bxsl_SpecialtyRetailSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Specialty Retail</link:label>
    <link:label id="lab_bxsl_SpecialtyRetailSectorMember_label_en-US" xlink:label="lab_bxsl_SpecialtyRetailSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Specialty Retail Sector [Member]</link:label>
    <link:label id="lab_bxsl_SpecialtyRetailSectorMember_documentation_en-US" xlink:label="lab_bxsl_SpecialtyRetailSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Specialty Retail Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_SpecialtyRetailSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_SpecialtyRetailSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_SpecialtyRetailSectorMember" xlink:to="lab_bxsl_SpecialtyRetailSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_019fd71c-09ae-7127-95fd-4881961c0fb3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_RelatedPartyTransactionTerminationNoticePeriod_019fd71c-091c-7ffc-b358-fc415f615737_terseLabel_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionTerminationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination notice period</link:label>
    <link:label id="lab_bxsl_RelatedPartyTransactionTerminationNoticePeriod_label_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionTerminationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Termination Notice Period</link:label>
    <link:label id="lab_bxsl_RelatedPartyTransactionTerminationNoticePeriod_documentation_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionTerminationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Termination Notice Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_RelatedPartyTransactionTerminationNoticePeriod" xlink:href="bxsl-20260930.xsd#bxsl_RelatedPartyTransactionTerminationNoticePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_RelatedPartyTransactionTerminationNoticePeriod" xlink:to="lab_bxsl_RelatedPartyTransactionTerminationNoticePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtPolicyTextBlock_019fd71c-09af-7a3b-be72-bf4b8860c79e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Financing Costs and Debt Issuance Costs</link:label>
    <link:label id="lab_us-gaap_DebtPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtPolicyTextBlock" xlink:to="lab_us-gaap_DebtPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019fd71c-0a16-7db3-8d77-6e2bff923db1_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019fd71c-09af-70d0-8e00-b843210107cf_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_019fd71c-091c-7570-ad50-5e31c2af2c9e_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_019fd71c-09af-7dba-8d45-81f90f281e3d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments/Forward Purchase Agreement</link:label>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesPolicyTextBlock" xlink:to="lab_us-gaap_DerivativesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019fd71c-09af-771a-b61b-25368eaee091_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
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    <link:label id="lab_bxsl_InterestRateSwap4Member_label_en-US" xlink:label="lab_bxsl_InterestRateSwap4Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 4 [Member]</link:label>
    <link:label id="lab_bxsl_InterestRateSwap4Member_documentation_en-US" xlink:label="lab_bxsl_InterestRateSwap4Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap 4</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InterestRateSwap4Member" xlink:href="bxsl-20260930.xsd#bxsl_InterestRateSwap4Member"/>
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    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_019fd71c-09ae-7c36-9a5e-fa1d0fc8fdd1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Derivative Liabilities Subject to Master Netting Agreement</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassCUnitsMember_01a186f1-f4d6-7707-a95c-81f392491cb7_terseLabel_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassCUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class C Units</link:label>
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    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassCUnitsMember_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassCUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class C Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassCUnitsMember" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassCUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassCUnitsMember" xlink:to="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassCUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_NetRealizedGainsLossesAbstract_019fd71c-09af-7c08-b25a-49607299f582_terseLabel_en-US" xlink:label="lab_bxsl_NetRealizedGainsLossesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized gain (loss):</link:label>
    <link:label id="lab_bxsl_NetRealizedGainsLossesAbstract_label_en-US" xlink:label="lab_bxsl_NetRealizedGainsLossesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Realized Gains (Losses) [Abstract]</link:label>
    <link:label id="lab_bxsl_NetRealizedGainsLossesAbstract_documentation_en-US" xlink:label="lab_bxsl_NetRealizedGainsLossesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Realized Gains (Losses)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_NetRealizedGainsLossesAbstract" xlink:href="bxsl-20260930.xsd#bxsl_NetRealizedGainsLossesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_NetRealizedGainsLossesAbstract" xlink:to="lab_bxsl_NetRealizedGainsLossesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_NonQualifyingAssetsMember_019fd71c-09af-7d39-9dfe-982de96071ec_terseLabel_en-US" xlink:label="lab_bxsl_NonQualifyingAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-qualifying Assets</link:label>
    <link:label id="lab_bxsl_NonQualifyingAssetsMember_label_en-US" xlink:label="lab_bxsl_NonQualifyingAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Qualifying Assets [Member]</link:label>
    <link:label id="lab_bxsl_NonQualifyingAssetsMember_documentation_en-US" xlink:label="lab_bxsl_NonQualifyingAssetsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Qualifying Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_NonQualifyingAssetsMember" xlink:href="bxsl-20260930.xsd#bxsl_NonQualifyingAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_NonQualifyingAssetsMember" xlink:to="lab_bxsl_NonQualifyingAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_019fd71c-09af-77f3-94bc-b2bb973debce_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Derivative liabilities at fair value (Note 6)</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_019fd71c-09af-7ad4-bdea-193e8f76f0c8_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net Amount Derivative Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, after Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyNetAssetsRollForward_019fd71c-09ae-7b6f-a9cc-d79e17a1b6c2_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyNetAssetsRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Company, Net Assets [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyNetAssetsRollForward_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyNetAssetsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Net Assets [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyNetAssetsRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyNetAssetsRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyNetAssetsRollForward" xlink:to="lab_us-gaap_InvestmentCompanyNetAssetsRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member_019fd71c-0a16-7e37-8685-726d114bc80e_terseLabel_en-US" xlink:label="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CitiBank, Revolving Credit Facility, Revolving Commitments 2027</link:label>
    <link:label id="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member_label_en-US" xlink:label="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CitiBank, Revolving Credit Facility, Revolving Commitments 2027 [Member]</link:label>
    <link:label id="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member_documentation_en-US" xlink:label="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CitiBank, Revolving Credit Facility, Revolving Commitments 2027</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member" xlink:href="bxsl-20260930.xsd#bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member" xlink:to="lab_bxsl_CitiBankRevolvingCreditFacilityRevolvingCommitments2027Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetNotionalAmount_019fd71c-09af-7f72-9a05-9359175adcb1_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetNotionalAmount" xlink:to="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage_019fd71c-09af-757a-88d6-0348c1d8e44d_terseLabel_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Annual catch up amount prior to the waiver period</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage_label_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Catch-Up Amount, Annualized Percentage</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage_documentation_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Catch-Up Amount, Annualized Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage" xlink:href="bxsl-20260930.xsd#bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage" xlink:to="lab_bxsl_IncomeBasedIncentiveFeesCatchUpAmountAnnualizedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossRatio_019fd71c-091c-77ef-aad6-bd53d12c8bb1_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ratio of net investment income to average net assets</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossRatio_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Investment Income (Loss) Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyInvestmentIncomeLossRatio" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyInvestmentIncomeLossRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyInvestmentIncomeLossRatio" xlink:to="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncentiveFeeExpenseIncomeBased_019fd71c-09af-7ee8-9598-4e20ddd53ff4_terseLabel_en-US" xlink:label="lab_us-gaap_IncentiveFeeExpenseIncomeBased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income based incentive fees (Note 3)</link:label>
    <link:label id="lab_us-gaap_IncentiveFeeExpenseIncomeBased_label_en-US" xlink:label="lab_us-gaap_IncentiveFeeExpenseIncomeBased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incentive Fee Expense, Income-Based</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncentiveFeeExpenseIncomeBased" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncentiveFeeExpenseIncomeBased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncentiveFeeExpenseIncomeBased" xlink:to="lab_us-gaap_IncentiveFeeExpenseIncomeBased" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_019fd71c-09af-7613-9b27-841921242bc8_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_SPVFinancingFacilitiesMember_019fd71c-09ae-7fad-8bb5-de9f5e5a7c87_terseLabel_en-US" xlink:label="lab_bxsl_SPVFinancingFacilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SPV Financing Facilities</link:label>
    <link:label id="lab_bxsl_SPVFinancingFacilitiesMember_label_en-US" xlink:label="lab_bxsl_SPVFinancingFacilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SPV Financing Facilities [Member]</link:label>
    <link:label id="lab_bxsl_SPVFinancingFacilitiesMember_documentation_en-US" xlink:label="lab_bxsl_SPVFinancingFacilitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">SPV Financing Facilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_SPVFinancingFacilitiesMember" xlink:href="bxsl-20260930.xsd#bxsl_SPVFinancingFacilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_SPVFinancingFacilitiesMember" xlink:to="lab_bxsl_SPVFinancingFacilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanySeniorSecurityIndebtednessAssetCoverageRatio_019fd71c-0a16-7a9a-b7fb-c730c91b7ccd_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanySeniorSecurityIndebtednessAssetCoverageRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset coverage ratio</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanySeniorSecurityIndebtednessAssetCoverageRatio_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanySeniorSecurityIndebtednessAssetCoverageRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Senior Security, Indebtedness, Asset Coverage Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanySeniorSecurityIndebtednessAssetCoverageRatio" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanySeniorSecurityIndebtednessAssetCoverageRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanySeniorSecurityIndebtednessAssetCoverageRatio" xlink:to="lab_us-gaap_InvestmentCompanySeniorSecurityIndebtednessAssetCoverageRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyDistributionPolicyTextBlock_019fd71c-09af-758e-bf7f-8a5778c42d57_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyDistributionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyDistributionPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyDistributionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Distribution [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyDistributionPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyDistributionPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyDistributionPolicyTextBlock" xlink:to="lab_us-gaap_InvestmentCompanyDistributionPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019fd71c-09ae-72d0-b864-fa36f71a7a11_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Basic and Diluted Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_019fd71c-0a16-70a5-b8d4-0536b39cf207_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_019fd71c-09ae-7608-9f7c-f416816159a4_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Low</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_019fd71c-09ae-7045-b93e-ba1ab351dd6a_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeAxis" xlink:to="lab_us-gaap_InvestmentTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DiversifiedTelecommunicationServicesSectorMember_019fd71c-09af-72a1-b8d8-c3138fe59b92_terseLabel_en-US" xlink:label="lab_bxsl_DiversifiedTelecommunicationServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diversified Telecommunication Services</link:label>
    <link:label id="lab_bxsl_DiversifiedTelecommunicationServicesSectorMember_label_en-US" xlink:label="lab_bxsl_DiversifiedTelecommunicationServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Diversified Telecommunication Services Sector [Member]</link:label>
    <link:label id="lab_bxsl_DiversifiedTelecommunicationServicesSectorMember_documentation_en-US" xlink:label="lab_bxsl_DiversifiedTelecommunicationServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Diversified Telecommunication Services Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DiversifiedTelecommunicationServicesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_DiversifiedTelecommunicationServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DiversifiedTelecommunicationServicesSectorMember" xlink:to="lab_bxsl_DiversifiedTelecommunicationServicesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsFairValueDisclosure_019fd71c-09ae-7aab-85c8-fe7d8a3846a2_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_InvestmentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_InvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsFairValueDisclosure" xlink:to="lab_us-gaap_InvestmentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019fd71c-09ae-7012-a35c-1cf799a8e43b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_019fd71c-09af-7392-ba10-76423fcbce88_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromInvestments_019fd71c-09ae-7ad1-8e18-6c5229212059_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Upfront Payments / Receipts</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForProceedsFromInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromInvestments" xlink:to="lab_us-gaap_PaymentsForProceedsFromInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_019fd71c-09af-762e-9baf-8747dbf99508_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_019fd71c-09ae-71a0-8008-113d51b21c3d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due to affiliates</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStock_019fd71c-09af-7c75-8879-867d24380212_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Amount</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStock" xlink:to="lab_us-gaap_DividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ElectricUtilitiesSectorMember_019fd71c-09ae-7f9b-be66-b992987a320b_terseLabel_en-US" xlink:label="lab_bxsl_ElectricUtilitiesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Electric Utilities</link:label>
    <link:label id="lab_bxsl_ElectricUtilitiesSectorMember_label_en-US" xlink:label="lab_bxsl_ElectricUtilitiesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Electric Utilities Sector [Member]</link:label>
    <link:label id="lab_bxsl_ElectricUtilitiesSectorMember_documentation_en-US" xlink:label="lab_bxsl_ElectricUtilitiesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Electric Utilities Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ElectricUtilitiesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_ElectricUtilitiesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ElectricUtilitiesSectorMember" xlink:to="lab_bxsl_ElectricUtilitiesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019fd71c-09ae-7d0b-819d-09e1b269162b_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_019fd71c-09af-7693-a73e-ffcf2318a681_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of common shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MeasurementInputMarketMultipleMember_019fd71c-09af-7cb2-8454-06623b94fbc2_terseLabel_en-US" xlink:label="lab_bxsl_MeasurementInputMarketMultipleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Market Multiple</link:label>
    <link:label id="lab_bxsl_MeasurementInputMarketMultipleMember_label_en-US" xlink:label="lab_bxsl_MeasurementInputMarketMultipleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Market Multiple [Member]</link:label>
    <link:label id="lab_bxsl_MeasurementInputMarketMultipleMember_documentation_en-US" xlink:label="lab_bxsl_MeasurementInputMarketMultipleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Market Multiple</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MeasurementInputMarketMultipleMember" xlink:href="bxsl-20260930.xsd#bxsl_MeasurementInputMarketMultipleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MeasurementInputMarketMultipleMember" xlink:to="lab_bxsl_MeasurementInputMarketMultipleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_019fd71c-09ae-77ee-8b67-36800d52c77f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value Measurements of Unsecured Notes</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Carrying Values and Estimated Fair Values of Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_019fd71c-0a16-7bd2-8608-b5e736222cc1_terseLabel_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock repurchase program authorized amount</link:label>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_label_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StockRepurchaseProgramAuthorizedAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:to="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A20241IssuerMember_019fd71c-0a16-70bc-98b1-cbfe03678058_terseLabel_en-US" xlink:label="lab_bxsl_A20241IssuerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024-1 Issuer</link:label>
    <link:label id="lab_bxsl_A20241IssuerMember_label_en-US" xlink:label="lab_bxsl_A20241IssuerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024-1 Issuer [Member]</link:label>
    <link:label id="lab_bxsl_A20241IssuerMember_documentation_en-US" xlink:label="lab_bxsl_A20241IssuerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024-1 Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A20241IssuerMember" xlink:href="bxsl-20260930.xsd#bxsl_A20241IssuerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A20241IssuerMember" xlink:to="lab_bxsl_A20241IssuerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_019fd71c-091c-731d-98c4-531b8b17bf5d_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree_019fd71c-09af-731a-95be-de84db0a0351_terseLabel_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">1 - 3 Years</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree_label_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term Maturities, Repayments of Principal in Rolling Year One Through Three</link:label>
    <link:label id="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree_documentation_en-US" xlink:label="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt, Long-Term and Short-Term Maturities, Repayments of Principal in Rolling Year One Through Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree" xlink:href="bxsl-20260930.xsd#bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree" xlink:to="lab_bxsl_DebtLongTermAndShortTermMaturitiesRepaymentsOfPrincipalInRollingYearOneThroughThree" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesRate_019fd71c-0a16-7f02-a167-9aadeee9a020_terseLabel_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income based incentive rate</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesRate_label_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Rate</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesRate_documentation_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_IncomeBasedIncentiveFeesRate" xlink:href="bxsl-20260930.xsd#bxsl_IncomeBasedIncentiveFeesRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_IncomeBasedIncentiveFeesRate" xlink:to="lab_bxsl_IncomeBasedIncentiveFeesRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EuropeMember_019fd71c-09ae-738a-9ce8-dd0fb4dc6eb3_terseLabel_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Europe</link:label>
    <link:label id="lab_srt_EuropeMember_label_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Europe [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EuropeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_EuropeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EuropeMember" xlink:to="lab_srt_EuropeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019fd71c-09ae-7e31-bef5-b177b92cafc2_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of foreign exchange rate changes on cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations"/>
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    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentOwnedFairValueMeasurementInput_019fd71c-09af-7b69-9822-4a65ee46a592_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentOwnedFairValueMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement input</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentOwnedFairValueMeasurementInput_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyInvestmentOwnedFairValueMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Investment Owned, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyInvestmentOwnedFairValueMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyInvestmentOwnedFairValueMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyInvestmentOwnedFairValueMeasurementInput" xlink:to="lab_us-gaap_InvestmentCompanyInvestmentOwnedFairValueMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedAtCost_019fd71c-09af-71fa-827f-00941dff7c70_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedAtCost_019fd71c-09af-77d5-85b3-b68093188146_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtCost" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Investment at cost</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedAtCost_label_en-US" xlink:label="lab_us-gaap_InvestmentOwnedAtCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedAtCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentOwnedAtCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentOwnedAtCost" xlink:to="lab_us-gaap_InvestmentOwnedAtCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossAdditions_019fd71c-091c-7e0e-8250-90e8857fedac_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossAdditions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Additions</link:label>
    <link:label id="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossAdditions_label_en-US" xlink:label="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in and Advances to Affiliates, at Fair Value, Gross Additions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossAdditions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossAdditions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossAdditions" xlink:to="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueGrossAdditions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019fd71c-09af-7bf9-9703-17246caacec3_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivableInvestmentSale_019fd71c-09af-7e71-a96b-3eae17080baa_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableInvestmentSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable for investments</link:label>
    <link:label id="lab_us-gaap_ReceivableInvestmentSale_label_en-US" xlink:label="lab_us-gaap_ReceivableInvestmentSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable, Investment, Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableInvestmentSale" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivableInvestmentSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivableInvestmentSale" xlink:to="lab_us-gaap_ReceivableInvestmentSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ManagementFeeExpense_019fd71c-091c-7b7e-b4ac-f49ebf282835_terseLabel_en-US" xlink:label="lab_us-gaap_ManagementFeeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fees (Note 3)</link:label>
    <link:label id="lab_us-gaap_ManagementFeeExpense_019fd71c-091c-7530-b9b9-aa84d94b130a_verboseLabel_en-US" xlink:label="lab_us-gaap_ManagementFeeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Management fees</link:label>
    <link:label id="lab_us-gaap_ManagementFeeExpense_label_en-US" xlink:label="lab_us-gaap_ManagementFeeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fee Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementFeeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ManagementFeeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ManagementFeeExpense" xlink:to="lab_us-gaap_ManagementFeeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncentiveFeeExpenseCapitalGainBased_019fd71c-091c-7ac4-9199-d3c4c88c6f43_terseLabel_en-US" xlink:label="lab_us-gaap_IncentiveFeeExpenseCapitalGainBased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital gains based incentive fees (Note 3)</link:label>
    <link:label id="lab_us-gaap_IncentiveFeeExpenseCapitalGainBased_label_en-US" xlink:label="lab_us-gaap_IncentiveFeeExpenseCapitalGainBased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incentive Fee Expense, Capital-Gain-Based</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncentiveFeeExpenseCapitalGainBased" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncentiveFeeExpenseCapitalGainBased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncentiveFeeExpenseCapitalGainBased" xlink:to="lab_us-gaap_IncentiveFeeExpenseCapitalGainBased" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_019fd71c-09af-7607-9c35-847eed3232f3_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:to="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputQuotedPriceMember_019fd71c-09af-7208-923f-12ffe0f587cb_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputQuotedPriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Broker quoted price</link:label>
    <link:label id="lab_us-gaap_MeasurementInputQuotedPriceMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputQuotedPriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Quoted Price [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputQuotedPriceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputQuotedPriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputQuotedPriceMember" xlink:to="lab_us-gaap_MeasurementInputQuotedPriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtSecuritiesFirstLienRealizedGainLossMember_019fd71c-0a16-7f2a-9998-4079e83c8882_terseLabel_en-US" xlink:label="lab_bxsl_DebtSecuritiesFirstLienRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, First Lien, Realized Gain (Loss)</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesFirstLienRealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_DebtSecuritiesFirstLienRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, First Lien, Realized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesFirstLienRealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_DebtSecuritiesFirstLienRealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, First Lien, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtSecuritiesFirstLienRealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_DebtSecuritiesFirstLienRealizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtSecuritiesFirstLienRealizedGainLossMember" xlink:to="lab_bxsl_DebtSecuritiesFirstLienRealizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyFinancialHighlightsTextBlock_019fd71c-09af-7dc0-a3a9-ee91a7024fda_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyFinancialHighlightsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Highlights and Senior Securities</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyFinancialHighlightsTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyFinancialHighlightsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Highlights [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyFinancialHighlightsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyFinancialHighlightsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyFinancialHighlightsTextBlock" xlink:to="lab_us-gaap_InvestmentCompanyFinancialHighlightsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_019fd71c-09ae-7057-a204-ee08d5c459a0_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt_019fd71c-09ae-7767-be24-e47f34212bc2_terseLabel_en-US" xlink:label="lab_bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average interest rate all-in</link:label>
    <link:label id="lab_bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt_label_en-US" xlink:label="lab_bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate, All In Cost Of Debt</link:label>
    <link:label id="lab_bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt_documentation_en-US" xlink:label="lab_bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate, All In Cost Of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt" xlink:href="bxsl-20260930.xsd#bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt" xlink:to="lab_bxsl_DebtWeightedAverageInterestRateAllInCostOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_019fd71c-091c-7e60-b0b1-dbc24ef39286_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_019fd71c-09af-7210-b0fa-8cc6e18dbabf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized gain (loss)</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_TrusteeFeesPayable_019fd71c-09af-7c5d-8081-493522e8d137_terseLabel_en-US" xlink:label="lab_bxsl_TrusteeFeesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Board of Trustees&#8217; fees payable</link:label>
    <link:label id="lab_bxsl_TrusteeFeesPayable_label_en-US" xlink:label="lab_bxsl_TrusteeFeesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trustee Fees Payable</link:label>
    <link:label id="lab_bxsl_TrusteeFeesPayable_documentation_en-US" xlink:label="lab_bxsl_TrusteeFeesPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Trustee Fees Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_TrusteeFeesPayable" xlink:href="bxsl-20260930.xsd#bxsl_TrusteeFeesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_TrusteeFeesPayable" xlink:to="lab_bxsl_TrusteeFeesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForPurchaseOfInvestmentOperatingActivity_019fd71c-0a16-74d8-b1af-e908a2fb6537_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForPurchaseOfInvestmentOperatingActivity" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of investments</link:label>
    <link:label id="lab_us-gaap_PaymentsForPurchaseOfInvestmentOperatingActivity_label_en-US" xlink:label="lab_us-gaap_PaymentsForPurchaseOfInvestmentOperatingActivity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Purchase, Investment, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForPurchaseOfInvestmentOperatingActivity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForPurchaseOfInvestmentOperatingActivity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForPurchaseOfInvestmentOperatingActivity" xlink:to="lab_us-gaap_PaymentsForPurchaseOfInvestmentOperatingActivity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignExchangeContractMember_019fd71c-09af-74e1-9b20-cfa5ded251b8_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignExchangeContractMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign Exchange Contract</link:label>
    <link:label id="lab_us-gaap_ForeignExchangeContractMember_label_en-US" xlink:label="lab_us-gaap_ForeignExchangeContractMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Exchange Contract [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignExchangeContractMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignExchangeContractMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignExchangeContractMember" xlink:to="lab_us-gaap_ForeignExchangeContractMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_019fd71c-09af-7d6d-aa2d-b26e316377b4_verboseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross proceeds</link:label>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_January2031NotesMember_019fd71c-09af-7aeb-b94b-79a3c201ba1b_terseLabel_en-US" xlink:label="lab_bxsl_January2031NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">January 2031 Notes</link:label>
    <link:label id="lab_bxsl_January2031NotesMember_label_en-US" xlink:label="lab_bxsl_January2031NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">January 2031 Notes [Member]</link:label>
    <link:label id="lab_bxsl_January2031NotesMember_documentation_en-US" xlink:label="lab_bxsl_January2031NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">January 2031 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_January2031NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_January2031NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_January2031NotesMember" xlink:to="lab_bxsl_January2031NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_019fd71c-09ae-7488-9a0f-52c55dfa6082_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ExciseTaxesPaid_019fd71c-09af-7f29-aeff-feca2986d6f5_terseLabel_en-US" xlink:label="lab_bxsl_ExciseTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excise and other taxes paid</link:label>
    <link:label id="lab_bxsl_ExciseTaxesPaid_label_en-US" xlink:label="lab_bxsl_ExciseTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Excise Taxes Paid</link:label>
    <link:label id="lab_bxsl_ExciseTaxesPaid_documentation_en-US" xlink:label="lab_bxsl_ExciseTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Excise Taxes Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ExciseTaxesPaid" xlink:href="bxsl-20260930.xsd#bxsl_ExciseTaxesPaid"/>
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    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_019fd71c-09af-743a-b841-e31a9f417c06_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Placement Fees/Offering Expenses</link:label>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Stock Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfStockIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OpenForwardForeignCurrencyContractLineItems_019fd71c-0a16-76e4-a7ab-554799a069d4_terseLabel_en-US" xlink:label="lab_us-gaap_OpenForwardForeignCurrencyContractLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Open Forward Foreign Currency Contract [Line Items]</link:label>
    <link:label id="lab_us-gaap_OpenForwardForeignCurrencyContractLineItems_label_en-US" xlink:label="lab_us-gaap_OpenForwardForeignCurrencyContractLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Open Forward Foreign Currency Contract [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OpenForwardForeignCurrencyContractLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OpenForwardForeignCurrencyContractLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OpenForwardForeignCurrencyContractLineItems" xlink:to="lab_us-gaap_OpenForwardForeignCurrencyContractLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_019fd71c-09af-7506-8206-ff60c9bb4612_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments on debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfDebt" xlink:to="lab_us-gaap_RepaymentsOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LetterOfCreditMember_019fd71c-091c-7234-93c1-13a4d9ff4208_terseLabel_en-US" xlink:label="lab_us-gaap_LetterOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letter of Credit</link:label>
    <link:label id="lab_us-gaap_LetterOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LetterOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letter of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LetterOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LetterOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LetterOfCreditMember" xlink:to="lab_us-gaap_LetterOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019fd71c-09ae-71c2-a887-8075576a1084_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember_019fd71c-09af-7945-aa16-6f6099452080_terseLabel_en-US" xlink:label="lab_bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Second Lien, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Second Lien, Unrealized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Second Lien, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember" xlink:to="lab_bxsl_DebtSecuritiesSecondLienUnrealizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember_019fd71c-09af-74cc-97ec-f2f406851c2f_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Management Agreement - Incentive Rate, Quarterly Hurdle Rate</link:label>
    <link:label id="lab_bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember_label_en-US" xlink:label="lab_bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Management Agreement - Incentive Rate, Quarterly Hurdle Rate Member [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Management Agreement - Incentive Rate, Quarterly Hurdle Rate Member</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember" xlink:to="lab_bxsl_InvestmentManagementAgreementIncentiveRateQuarterlyHurdleRateMemberMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_019fd71c-0a16-711f-b75c-a82192381cf1_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio_019fd71c-09ae-739e-85d1-b0efc5b14c15_terseLabel_en-US" xlink:label="lab_bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset coverage ratio</link:label>
    <link:label id="lab_bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio_label_en-US" xlink:label="lab_bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant Compliance, Required Asset Coverage Ratio</link:label>
    <link:label id="lab_bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio_documentation_en-US" xlink:label="lab_bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant Compliance, Required Asset Coverage Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio" xlink:href="bxsl-20260930.xsd#bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio" xlink:to="lab_bxsl_DebtInstrumentCovenantComplianceRequiredAssetCoverageRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_019fd71c-09af-7a20-ac19-064d9b847938_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:to="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019fd71c-0a16-7160-9e4b-325ef201c6aa_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
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    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_019fd71c-09af-7a86-af5d-9e01b5a37fec_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NET ASSETS</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityAbstract" xlink:to="lab_us-gaap_StockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember_019fd71c-09af-70fd-89c5-9bba263d5368_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Management Agreement - Incentive Rate, Annualized Hurdle Rate</link:label>
    <link:label id="lab_bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember_label_en-US" xlink:label="lab_bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Management Agreement - Incentive Rate, Annualized Hurdle Rate Member [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Management Agreement - Incentive Rate, Annualized Hurdle Rate Member</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember" xlink:to="lab_bxsl_InvestmentManagementAgreementIncentiveRateAnnualizedHurdleRateMemberMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019fd71c-091c-78a3-afab-158d7fe0a5f8_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyTaxReturnOfCapitalDistributionPerShare_019fd71c-09ae-7264-b76d-9cba694ee04e_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyTaxReturnOfCapitalDistributionPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in net assets from capital share transactions (in usd per share)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyTaxReturnOfCapitalDistributionPerShare_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyTaxReturnOfCapitalDistributionPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Tax Return of Capital Distribution, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyTaxReturnOfCapitalDistributionPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyTaxReturnOfCapitalDistributionPerShare"/>
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    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Foreign Currency Transaction, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax"/>
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    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsDomain_019fd71c-09af-791b-a901-c2be83e3e60c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Domain]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsDomain_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsDomain" xlink:to="lab_us-gaap_OtherCommitmentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentBasisSpreadVariableRate_019fd71c-0a16-780e-bfcd-0591348460d6_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentBasisSpreadVariableRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, basis spread, variable rate</link:label>
    <link:label id="lab_us-gaap_InvestmentBasisSpreadVariableRate_label_en-US" xlink:label="lab_us-gaap_InvestmentBasisSpreadVariableRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Basis Spread, Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentBasisSpreadVariableRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentBasisSpreadVariableRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentBasisSpreadVariableRate" xlink:to="lab_us-gaap_InvestmentBasisSpreadVariableRate" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019fd71c-0a16-7f62-bfae-9bdf52b0adf1_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_May2031NotesMember_019fd71c-0a16-7961-8ce7-083325e30969_terseLabel_en-US" xlink:label="lab_bxsl_May2031NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">May 2031 Notes</link:label>
    <link:label id="lab_bxsl_May2031NotesMember_label_en-US" xlink:label="lab_bxsl_May2031NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">May 2031 Notes [Member]</link:label>
    <link:label id="lab_bxsl_May2031NotesMember_documentation_en-US" xlink:label="lab_bxsl_May2031NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">May 2031 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_May2031NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_May2031NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_May2031NotesMember" xlink:to="lab_bxsl_May2031NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MeasurementInputPerformanceMultipleMember_019fd71c-09af-76e8-b589-fcfca845b20d_terseLabel_en-US" xlink:label="lab_bxsl_MeasurementInputPerformanceMultipleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Multiple</link:label>
    <link:label id="lab_bxsl_MeasurementInputPerformanceMultipleMember_label_en-US" xlink:label="lab_bxsl_MeasurementInputPerformanceMultipleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Performance Multiple [Member]</link:label>
    <link:label id="lab_bxsl_MeasurementInputPerformanceMultipleMember_documentation_en-US" xlink:label="lab_bxsl_MeasurementInputPerformanceMultipleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Performance Multiple</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MeasurementInputPerformanceMultipleMember" xlink:href="bxsl-20260930.xsd#bxsl_MeasurementInputPerformanceMultipleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MeasurementInputPerformanceMultipleMember" xlink:to="lab_bxsl_MeasurementInputPerformanceMultipleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_019fd71c-09ae-7668-8915-c0a3b495c9a0_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_019fd71c-09af-7de7-bf3d-d74927549ac4_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected Volatility</link:label>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Price Volatility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputPriceVolatilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:to="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCClassA3UnitsMember_019fd71c-09ae-766f-85ef-5e8b36ed43aa_terseLabel_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCClassA3UnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - Class A-3 Units</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCClassA3UnitsMember_label_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCClassA3UnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - Class A-3 Units [Member]</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCClassA3UnitsMember_documentation_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCClassA3UnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - Class A-3 Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AlignPrecisionGroupLLCClassA3UnitsMember" xlink:href="bxsl-20260930.xsd#bxsl_AlignPrecisionGroupLLCClassA3UnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AlignPrecisionGroupLLCClassA3UnitsMember" xlink:to="lab_bxsl_AlignPrecisionGroupLLCClassA3UnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_PaperForestProductsSectorMember_019fd71c-0a16-7817-af64-edf4bb2f96bf_terseLabel_en-US" xlink:label="lab_bxsl_PaperForestProductsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Paper &amp; Forest Products</link:label>
    <link:label id="lab_bxsl_PaperForestProductsSectorMember_label_en-US" xlink:label="lab_bxsl_PaperForestProductsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Paper &amp; Forest Products Sector [Member]</link:label>
    <link:label id="lab_bxsl_PaperForestProductsSectorMember_documentation_en-US" xlink:label="lab_bxsl_PaperForestProductsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Paper &amp; Forest Products Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_PaperForestProductsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_PaperForestProductsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_PaperForestProductsSectorMember" xlink:to="lab_bxsl_PaperForestProductsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AerospaceAndDefenseSectorMember_019fd71c-09af-7dad-8343-c672d59d0214_terseLabel_en-US" xlink:label="lab_bxsl_AerospaceAndDefenseSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aerospace &amp; Defense</link:label>
    <link:label id="lab_bxsl_AerospaceAndDefenseSectorMember_label_en-US" xlink:label="lab_bxsl_AerospaceAndDefenseSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aerospace And Defense Sector [Member]</link:label>
    <link:label id="lab_bxsl_AerospaceAndDefenseSectorMember_documentation_en-US" xlink:label="lab_bxsl_AerospaceAndDefenseSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Aerospace And Defense Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AerospaceAndDefenseSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_AerospaceAndDefenseSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AerospaceAndDefenseSectorMember" xlink:to="lab_bxsl_AerospaceAndDefenseSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019fd71c-09af-771e-ba54-6cd96ff0887b_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentCompanyPerShareDataAbstract_019fd71c-09af-747a-ab2b-bedaf8d6a99f_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentCompanyPerShareDataAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Company, Per Share Data [Abstract]</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyPerShareDataAbstract_label_en-US" xlink:label="lab_bxsl_InvestmentCompanyPerShareDataAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Per Share Data [Abstract]</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyPerShareDataAbstract_documentation_en-US" xlink:label="lab_bxsl_InvestmentCompanyPerShareDataAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Per Share Data</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentCompanyPerShareDataAbstract" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentCompanyPerShareDataAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentCompanyPerShareDataAbstract" xlink:to="lab_bxsl_InvestmentCompanyPerShareDataAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A5.300NotesDue2030Member_019fd71c-09af-723a-bc6a-f0bdc757114e_terseLabel_en-US" xlink:label="lab_bxsl_A5.300NotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.300% Notes Due 2030</link:label>
    <link:label id="lab_bxsl_A5.300NotesDue2030Member_label_en-US" xlink:label="lab_bxsl_A5.300NotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5.300% Notes Due 2030 [Member]</link:label>
    <link:label id="lab_bxsl_A5.300NotesDue2030Member_documentation_en-US" xlink:label="lab_bxsl_A5.300NotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5.300% Notes Due 2030</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A5.300NotesDue2030Member" xlink:href="bxsl-20260930.xsd#bxsl_A5.300NotesDue2030Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A5.300NotesDue2030Member" xlink:to="lab_bxsl_A5.300NotesDue2030Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyMarketValuePerShare_019fd71c-09af-7fa0-b17d-d76371afa778_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyMarketValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Market value, end of period (in usd per share)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyMarketValuePerShare_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyMarketValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Market Value, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyMarketValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyMarketValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyMarketValuePerShare" xlink:to="lab_us-gaap_InvestmentCompanyMarketValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member_019fd71c-0a16-7f0e-96dd-7a6208599d5b_terseLabel_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - First Lien Debt</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member_label_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - First Lien Debt 1 [Member]</link:label>
    <link:label id="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member_documentation_en-US" xlink:label="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Align Precision Group, LLC - First Lien Debt 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member" xlink:href="bxsl-20260930.xsd#bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member" xlink:to="lab_bxsl_AlignPrecisionGroupLLCFirstLienDebt1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember_01a186f2-6ae4-7200-858d-edba80fab695_terseLabel_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class A Preferred Units</link:label>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember_label_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class A Preferred Units [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Equity and other - Class A Preferred Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember" xlink:to="lab_bxsl_MaterialHoldingCompanyLLCEquityAndOtherClassAPreferredUnitsMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_bxsl_UnrealizedGainLossDerivativeOperatingAfterTax_label_en-US" xlink:label="lab_bxsl_UnrealizedGainLossDerivativeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss), Derivative, Operating, After Tax</link:label>
    <link:label id="lab_bxsl_UnrealizedGainLossDerivativeOperatingAfterTax_documentation_en-US" xlink:label="lab_bxsl_UnrealizedGainLossDerivativeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss), Derivative, Operating, After Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_UnrealizedGainLossDerivativeOperatingAfterTax" xlink:href="bxsl-20260930.xsd#bxsl_UnrealizedGainLossDerivativeOperatingAfterTax"/>
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    <link:label id="lab_bxsl_MaterialHoldingsLLCFirstLienDebt1Member_label_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLCFirstLienDebt1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC - First Lien Debt 1 [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLCFirstLienDebt1Member_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLCFirstLienDebt1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC - First Lien Debt 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingsLLCFirstLienDebt1Member" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingsLLCFirstLienDebt1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MaterialHoldingsLLCFirstLienDebt1Member" xlink:to="lab_bxsl_MaterialHoldingsLLCFirstLienDebt1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_BreckenridgeFundingFacilityMember_019fd71c-09ae-70bb-9daa-aa9a2b50c625_terseLabel_en-US" xlink:label="lab_bxsl_BreckenridgeFundingFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Breckenridge Funding Facility</link:label>
    <link:label id="lab_bxsl_BreckenridgeFundingFacilityMember_label_en-US" xlink:label="lab_bxsl_BreckenridgeFundingFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Breckenridge Funding Facility [Member]</link:label>
    <link:label id="lab_bxsl_BreckenridgeFundingFacilityMember_documentation_en-US" xlink:label="lab_bxsl_BreckenridgeFundingFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Breckenridge Funding Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_BreckenridgeFundingFacilityMember" xlink:href="bxsl-20260930.xsd#bxsl_BreckenridgeFundingFacilityMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfSaleOfStockBySubsidiaryOrEquityMethodInvesteeDisclosureTextBlock_019fd71c-0a16-7280-a8c9-642b2c552df7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSaleOfStockBySubsidiaryOrEquityMethodInvesteeDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Shares Issued and Proceeds Received</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSaleOfStockBySubsidiaryOrEquityMethodInvesteeDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSaleOfStockBySubsidiaryOrEquityMethodInvesteeDisclosureTextBlock"/>
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    <link:label id="lab_bxsl_MedalliaInc.FirstLienDebt2Member_01a17cdb-ed03-7d77-8d86-54e19d7c9ed3_terseLabel_en-US" xlink:label="lab_bxsl_MedalliaInc.FirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Medallia, Inc. - First Lien Debt</link:label>
    <link:label id="lab_bxsl_MedalliaInc.FirstLienDebt2Member_label_en-US" xlink:label="lab_bxsl_MedalliaInc.FirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Medallia, Inc. - First Lien Debt 2 [Member]</link:label>
    <link:label id="lab_bxsl_MedalliaInc.FirstLienDebt2Member_documentation_en-US" xlink:label="lab_bxsl_MedalliaInc.FirstLienDebt2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Medallia, Inc. - First Lien Debt 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MedalliaInc.FirstLienDebt2Member" xlink:href="bxsl-20260930.xsd#bxsl_MedalliaInc.FirstLienDebt2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MedalliaInc.FirstLienDebt2Member" xlink:to="lab_bxsl_MedalliaInc.FirstLienDebt2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedBalancePrincipalAmount_019fd71c-0a16-7417-8100-6fcb1e0e11b6_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedBalancePrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment owned, balance, principal amount</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedBalancePrincipalAmount_label_en-US" xlink:label="lab_us-gaap_InvestmentOwnedBalancePrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Balance, Principal Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedBalancePrincipalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentOwnedBalancePrincipalAmount"/>
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    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_019fd71c-09af-7fdd-9686-b5d0bbc232d2_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Appreciation (Depreciation)</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_019fd71c-09af-7472-97b5-f7016ee51ba7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Derivatives Available for Offset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Liability Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetFairValueGrossLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:to="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_GroundTransportationSectorMember_019fd71c-09ae-7ac2-ab9f-ec7c5b93105f_terseLabel_en-US" xlink:label="lab_bxsl_GroundTransportationSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ground Transportation</link:label>
    <link:label id="lab_bxsl_GroundTransportationSectorMember_label_en-US" xlink:label="lab_bxsl_GroundTransportationSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ground Transportation Sector [Member]</link:label>
    <link:label id="lab_bxsl_GroundTransportationSectorMember_documentation_en-US" xlink:label="lab_bxsl_GroundTransportationSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ground Transportation Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_GroundTransportationSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_GroundTransportationSectorMember"/>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_019fd71c-09af-715c-9fc6-1697ac3b5056_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems"/>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtWeightedAverageInterestRateOverTime_019fd71c-09af-7e43-b740-b7faa10f94b5_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtWeightedAverageInterestRateOverTime" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average interest rate</link:label>
    <link:label id="lab_us-gaap_LongTermDebtWeightedAverageInterestRateOverTime_label_en-US" xlink:label="lab_us-gaap_LongTermDebtWeightedAverageInterestRateOverTime" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Weighted Average Interest Rate, over Time</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtWeightedAverageInterestRateOverTime" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtWeightedAverageInterestRateOverTime"/>
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    <link:label id="lab_us-gaap_StockholdersEquityPolicyTextBlock_019fd71c-09af-703b-ad83-5a0016e84d89_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offering Expenses</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stockholders' Equity, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_InvestmentCompanyAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyAbstract"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompRecoveryTable"/>
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    <link:label id="lab_bxsl_PharmaceuticalsSectorMember_label_en-US" xlink:label="lab_bxsl_PharmaceuticalsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pharmaceuticals Sector [Member]</link:label>
    <link:label id="lab_bxsl_PharmaceuticalsSectorMember_documentation_en-US" xlink:label="lab_bxsl_PharmaceuticalsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Pharmaceuticals Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_PharmaceuticalsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_PharmaceuticalsSectorMember"/>
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    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019fd71c-09af-7373-8ca5-f791dac66829_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019fd71c-091c-7c08-8b53-f23a2be54201_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ConstructionEngineeringSectorMember_019fd71c-09af-716b-b6ef-67fee32d33e8_terseLabel_en-US" xlink:label="lab_bxsl_ConstructionEngineeringSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Construction &amp; Engineering</link:label>
    <link:label id="lab_bxsl_ConstructionEngineeringSectorMember_label_en-US" xlink:label="lab_bxsl_ConstructionEngineeringSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction &amp; Engineering Sector [Member]</link:label>
    <link:label id="lab_bxsl_ConstructionEngineeringSectorMember_documentation_en-US" xlink:label="lab_bxsl_ConstructionEngineeringSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Construction &amp; Engineering Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ConstructionEngineeringSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_ConstructionEngineeringSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ConstructionEngineeringSectorMember" xlink:to="lab_bxsl_ConstructionEngineeringSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AutomobileComponentsSectorMember_019fd71c-09ae-7291-a9a9-0b4a30b9eb2b_terseLabel_en-US" xlink:label="lab_bxsl_AutomobileComponentsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Automobile Components</link:label>
    <link:label id="lab_bxsl_AutomobileComponentsSectorMember_label_en-US" xlink:label="lab_bxsl_AutomobileComponentsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Automobile Components Sector [Member]</link:label>
    <link:label id="lab_bxsl_AutomobileComponentsSectorMember_documentation_en-US" xlink:label="lab_bxsl_AutomobileComponentsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Automobile Components Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AutomobileComponentsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_AutomobileComponentsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AutomobileComponentsSectorMember" xlink:to="lab_bxsl_AutomobileComponentsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyTotalReturn_019fd71c-09af-7077-bb8a-fffc30c363d0_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyTotalReturn" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total return based on NAV</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyTotalReturn_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyTotalReturn" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Total Return</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyTotalReturn" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyTotalReturn"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyTotalReturn" xlink:to="lab_us-gaap_InvestmentCompanyTotalReturn" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A2850NotesDue2028Member_019fd71c-09af-78c0-87ce-816253e4e380_terseLabel_en-US" xlink:label="lab_bxsl_A2850NotesDue2028Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2.850% Notes Due 2028</link:label>
    <link:label id="lab_bxsl_A2850NotesDue2028Member_label_en-US" xlink:label="lab_bxsl_A2850NotesDue2028Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2.850% Notes Due 2028 [Member]</link:label>
    <link:label id="lab_bxsl_A2850NotesDue2028Member_documentation_en-US" xlink:label="lab_bxsl_A2850NotesDue2028Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2.850% Notes Due 2028</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A2850NotesDue2028Member" xlink:href="bxsl-20260930.xsd#bxsl_A2850NotesDue2028Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A2850NotesDue2028Member" xlink:to="lab_bxsl_A2850NotesDue2028Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ChemicalsSectorMember_019fd71c-0a16-7fb9-96ec-3be3b71dca53_terseLabel_en-US" xlink:label="lab_us-gaap_ChemicalsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Chemicals</link:label>
    <link:label id="lab_us-gaap_ChemicalsSectorMember_label_en-US" xlink:label="lab_us-gaap_ChemicalsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Chemicals Sector [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ChemicalsSectorMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ChemicalsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ChemicalsSectorMember" xlink:to="lab_us-gaap_ChemicalsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019fd71c-09ae-71aa-af34-dee3fa3e48ac_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net increase (decrease) in net assets resulting from operations to net cash provided by (used in) operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019fd71c-09af-7432-bf76-b7fe4add55d3_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember_019fd71c-09af-75a7-9324-a84b0a18aa6e_terseLabel_en-US" xlink:label="lab_bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class A Notes, Senior Secured Floating Rate</link:label>
    <link:label id="lab_bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember_label_en-US" xlink:label="lab_bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class A Notes, Senior Secured Floating Rate [Member]</link:label>
    <link:label id="lab_bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember_documentation_en-US" xlink:label="lab_bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class A Notes, Senior Secured Floating Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember" xlink:href="bxsl-20260930.xsd#bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember" xlink:to="lab_bxsl_A20241CLOClassANotesSeniorSecuredFloatingRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_019fd71c-09af-7e16-b992-79b6929ae919_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unused capacity, commitment fee percentage</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:to="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier_019fd71c-09af-710c-a14b-1dbb95bf996f_terseLabel_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Combined revolving debt amount multiplier</link:label>
    <link:label id="lab_bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier_label_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Combined Revolving Debt Amount, Multiplier</link:label>
    <link:label id="lab_bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier_documentation_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Combined Revolving Debt Amount, Multiplier</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier" xlink:href="bxsl-20260930.xsd#bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier" xlink:to="lab_bxsl_LineOfCreditFacilityCombinedRevolvingDebtAmountMultiplier" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019fd71c-0a16-77d2-b59c-e8b556a654f0_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_cef_SeniorSecuritiesTableTextBlock_019fd71c-09af-757e-8a0d-be1fd4320719_terseLabel_en-US" xlink:label="lab_cef_SeniorSecuritiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Senior Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_cef_SeniorSecuritiesTableTextBlock" xlink:href="https://xbrl.sec.gov/cef/2026/cef-2026.xsd#cef_SeniorSecuritiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_cef_SeniorSecuritiesTableTextBlock" xlink:to="lab_cef_SeniorSecuritiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_019fd71c-0a16-75cc-a8a3-c0820d952686_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Derivative asset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A5.250NotesDue2029Member_019fd71c-09ae-763d-a488-3bc142c63f67_terseLabel_en-US" xlink:label="lab_bxsl_A5.250NotesDue2029Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.250% Notes Due 2029</link:label>
    <link:label id="lab_bxsl_A5.250NotesDue2029Member_label_en-US" xlink:label="lab_bxsl_A5.250NotesDue2029Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5.250% Notes Due 2029 [Member]</link:label>
    <link:label id="lab_bxsl_A5.250NotesDue2029Member_documentation_en-US" xlink:label="lab_bxsl_A5.250NotesDue2029Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5.250% Notes Due 2029</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A5.250NotesDue2029Member" xlink:href="bxsl-20260930.xsd#bxsl_A5.250NotesDue2029Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A5.250NotesDue2029Member" xlink:to="lab_bxsl_A5.250NotesDue2029Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_019fd71c-091c-7ac1-a797-753f6e96024d_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Common Shares, net of offering and underwriting costs</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock_019fd71c-0a16-7dc6-b3ff-a3f2eaf385d5_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financial Highlights</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Highlights [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock" xlink:to="lab_us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_DebtSecuritizationsMember_019fd71c-09af-72b1-8e66-04d1e4dc8b6d_terseLabel_en-US" xlink:label="lab_bxsl_DebtSecuritizationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securitizations</link:label>
    <link:label id="lab_bxsl_DebtSecuritizationsMember_label_en-US" xlink:label="lab_bxsl_DebtSecuritizationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securitizations [Member]</link:label>
    <link:label id="lab_bxsl_DebtSecuritizationsMember_documentation_en-US" xlink:label="lab_bxsl_DebtSecuritizationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securitizations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_DebtSecuritizationsMember" xlink:href="bxsl-20260930.xsd#bxsl_DebtSecuritizationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_DebtSecuritizationsMember" xlink:to="lab_bxsl_DebtSecuritizationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_OilGasConsumableFuelsSectorMember_019fd71c-0a16-7630-b786-81b6483ab7f2_terseLabel_en-US" xlink:label="lab_bxsl_OilGasConsumableFuelsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Oil, Gas &amp; Consumable Fuels</link:label>
    <link:label id="lab_bxsl_OilGasConsumableFuelsSectorMember_label_en-US" xlink:label="lab_bxsl_OilGasConsumableFuelsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil, Gas &amp; Consumable Fuels Sector [Member]</link:label>
    <link:label id="lab_bxsl_OilGasConsumableFuelsSectorMember_documentation_en-US" xlink:label="lab_bxsl_OilGasConsumableFuelsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Oil, Gas &amp; Consumable Fuels Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_OilGasConsumableFuelsSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_OilGasConsumableFuelsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_OilGasConsumableFuelsSectorMember" xlink:to="lab_bxsl_OilGasConsumableFuelsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCClassCUnitsMember_019fd71c-09af-7982-9638-e493ac72e4fe_terseLabel_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCClassCUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Class C Units</link:label>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCClassCUnitsMember_label_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCClassCUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Class C Units [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingCompanyLLCClassCUnitsMember_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingCompanyLLCClassCUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material+ Holding Company, LLC - Class C Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingCompanyLLCClassCUnitsMember" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingCompanyLLCClassCUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MaterialHoldingCompanyLLCClassCUnitsMember" xlink:to="lab_bxsl_MaterialHoldingCompanyLLCClassCUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers_019fd71c-09ae-7f76-af3c-ed46015f1b61_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of borrowers</link:label>
    <link:label id="lab_bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers_label_en-US" xlink:label="lab_bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Nonaccrual, Number Of Borrowers</link:label>
    <link:label id="lab_bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers_documentation_en-US" xlink:label="lab_bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Owned, Nonaccrual, Number Of Borrowers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers" xlink:to="lab_bxsl_InvestmentOwnedNonaccrualNumberOfBorrowers" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_RevolvingCommitmentsMember_019fd71c-09ae-7975-9fb7-19a70ca8e3a5_terseLabel_en-US" xlink:label="lab_bxsl_RevolvingCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Commitments</link:label>
    <link:label id="lab_bxsl_RevolvingCommitmentsMember_label_en-US" xlink:label="lab_bxsl_RevolvingCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Commitments [Member]</link:label>
    <link:label id="lab_bxsl_RevolvingCommitmentsMember_documentation_en-US" xlink:label="lab_bxsl_RevolvingCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revolving Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_RevolvingCommitmentsMember" xlink:href="bxsl-20260930.xsd#bxsl_RevolvingCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_RevolvingCommitmentsMember" xlink:to="lab_bxsl_RevolvingCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019fd71c-09af-722a-b1f7-254582d78d0f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions, by Related Party [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019fd71c-09af-78cc-9939-6e732788c394_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesScenarioAxis_019fd71c-09af-7d9e-91b8-273c973b73e1_terseLabel_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Scenario [Axis]</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesScenarioAxis_label_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Scenario [Axis]</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesScenarioAxis_documentation_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Scenario</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_IncomeBasedIncentiveFeesScenarioAxis" xlink:href="bxsl-20260930.xsd#bxsl_IncomeBasedIncentiveFeesScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_IncomeBasedIncentiveFeesScenarioAxis" xlink:to="lab_bxsl_IncomeBasedIncentiveFeesScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedBalanceShares_019fd71c-09ae-78ec-8f48-050a80fb7995_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedBalanceShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment owned (in shares)</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedBalanceShares_label_en-US" xlink:label="lab_us-gaap_InvestmentOwnedBalanceShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Balance, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedBalanceShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentOwnedBalanceShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentOwnedBalanceShares" xlink:to="lab_us-gaap_InvestmentOwnedBalanceShares" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLineItems_019fd71c-09af-7920-a69e-e3d4c5b821ed_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_AsiaMember_019fd71c-0a16-7eb1-934d-0258c0e25654_terseLabel_en-US" xlink:label="lab_srt_AsiaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asia</link:label>
    <link:label id="lab_srt_AsiaMember_label_en-US" xlink:label="lab_srt_AsiaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asia [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AsiaMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_AsiaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_AsiaMember" xlink:to="lab_srt_AsiaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialServicesSectorMember_019fd71c-09af-7774-87c4-4bbfbe910997_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Services</link:label>
    <link:label id="lab_us-gaap_FinancialServicesSectorMember_label_en-US" xlink:label="lab_us-gaap_FinancialServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Services Sector [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialServicesSectorMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialServicesSectorMember" xlink:to="lab_us-gaap_FinancialServicesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_019fd71c-09ae-7103-ab42-9c20c7a390c6_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares repurchased (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_019fd71c-0a16-7bd8-b371-57c673d1e4f6_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Per share amount (in usd per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ConsumerStaplesDistributionAndRetailSectorMember_019fd71c-091c-7b11-b09f-f9cfaead4385_terseLabel_en-US" xlink:label="lab_bxsl_ConsumerStaplesDistributionAndRetailSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consumer Staples Distribution And Retail</link:label>
    <link:label id="lab_bxsl_ConsumerStaplesDistributionAndRetailSectorMember_label_en-US" xlink:label="lab_bxsl_ConsumerStaplesDistributionAndRetailSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consumer Staples Distribution And Retail Sector [Member]</link:label>
    <link:label id="lab_bxsl_ConsumerStaplesDistributionAndRetailSectorMember_documentation_en-US" xlink:label="lab_bxsl_ConsumerStaplesDistributionAndRetailSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Consumer Staples Distribution And Retail Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ConsumerStaplesDistributionAndRetailSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_ConsumerStaplesDistributionAndRetailSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ConsumerStaplesDistributionAndRetailSectorMember" xlink:to="lab_bxsl_ConsumerStaplesDistributionAndRetailSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019fd71c-0a16-7275-8339-84af7030b49a_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities Act File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_AtTheMarketOfferingOffering1Member_019fd71c-09ae-71cd-92c1-9a10543f2ea7_terseLabel_en-US" xlink:label="lab_bxsl_AtTheMarketOfferingOffering1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">At-the-Market Offering, Offering</link:label>
    <link:label id="lab_bxsl_AtTheMarketOfferingOffering1Member_label_en-US" xlink:label="lab_bxsl_AtTheMarketOfferingOffering1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">At-the-Market Offering, Offering 1 [Member]</link:label>
    <link:label id="lab_bxsl_AtTheMarketOfferingOffering1Member_documentation_en-US" xlink:label="lab_bxsl_AtTheMarketOfferingOffering1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">At-the-Market Offering, Offering 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_AtTheMarketOfferingOffering1Member" xlink:href="bxsl-20260930.xsd#bxsl_AtTheMarketOfferingOffering1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_AtTheMarketOfferingOffering1Member" xlink:to="lab_bxsl_AtTheMarketOfferingOffering1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome_019fd71c-09af-7a88-b840-cc0b109aa517_terseLabel_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payment of pre incentive rate investment income, percentage</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome_label_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Percentage Of Pre-Incentive Fee Net Investment Income</link:label>
    <link:label id="lab_bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome_documentation_en-US" xlink:label="lab_bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Based Incentive Fees, Percentage Of Pre-Incentive Fee Net Investment Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome" xlink:href="bxsl-20260930.xsd#bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome" xlink:to="lab_bxsl_IncomeBasedIncentiveFeesPercentageOfPreIncentiveFeeNetInvestmentIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember_019fd71c-09af-78b8-a79f-61fe28c6281c_terseLabel_en-US" xlink:label="lab_bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class B Notes, Senior Secured Floating Rate</link:label>
    <link:label id="lab_bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember_label_en-US" xlink:label="lab_bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class B Notes, Senior Secured Floating Rate [Member]</link:label>
    <link:label id="lab_bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember_documentation_en-US" xlink:label="lab_bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class B Notes, Senior Secured Floating Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember" xlink:href="bxsl-20260930.xsd#bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember" xlink:to="lab_bxsl_A20241CLOClassBNotesSeniorSecuredFloatingRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019fd71c-09ae-77fb-a50e-6bf3f596ca79_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax_019fd71c-09ae-777b-8c2f-82f78cd5943a_totalLabel_en-US" xlink:label="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net realized gain (loss), net of tax expense</link:label>
    <link:label id="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax_019fd71c-09ae-720a-893c-323d3b5c92ed_terseLabel_en-US" xlink:label="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized gain (loss), net of tax expense</link:label>
    <link:label id="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax_label_en-US" xlink:label="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Investment, Derivative, and Foreign Currency Transaction Price Change, Operating, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:to="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019fd71c-09ae-76c4-bea7-376621571e70_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateAxis_019fd71c-09af-70d9-b692-914e4a058ba8_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:label id="lab_us-gaap_VariableRateAxis_label_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableRateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateAxis" xlink:to="lab_us-gaap_VariableRateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtIssuanceCostsLineOfCreditArrangementsNet_019fd71c-09af-7800-abd0-3146c8ed7892_terseLabel_en-US" xlink:label="lab_us-gaap_DebtIssuanceCostsLineOfCreditArrangementsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred financing costs</link:label>
    <link:label id="lab_us-gaap_DebtIssuanceCostsLineOfCreditArrangementsNet_label_en-US" xlink:label="lab_us-gaap_DebtIssuanceCostsLineOfCreditArrangementsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Line of Credit Arrangements, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtIssuanceCostsLineOfCreditArrangementsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtIssuanceCostsLineOfCreditArrangementsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtIssuanceCostsLineOfCreditArrangementsNet" xlink:to="lab_us-gaap_DebtIssuanceCostsLineOfCreditArrangementsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019fd71c-09af-7b09-8be1-662bfc069bbf_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DistributionPayable_019fd71c-09af-7625-99f1-db435f4d387c_terseLabel_en-US" xlink:label="lab_us-gaap_DistributionPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distribution payable</link:label>
    <link:label id="lab_us-gaap_DistributionPayable_label_en-US" xlink:label="lab_us-gaap_DistributionPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Distribution Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DistributionPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DistributionPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DistributionPayable" xlink:to="lab_us-gaap_DistributionPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_019fd71c-09ae-7b0b-9b3a-56eb1207b661_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets at fair value (Note 6)</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_019fd71c-09ae-70c4-a062-7c651eedaa06_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Amount Derivative Asset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, after Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromDispositionOfInvestmentOperatingActivity_019fd71c-09af-7ee4-b8ec-09fde4dab272_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromDispositionOfInvestmentOperatingActivity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of investments and principal repayments</link:label>
    <link:label id="lab_us-gaap_ProceedsFromDispositionOfInvestmentOperatingActivity_label_en-US" xlink:label="lab_us-gaap_ProceedsFromDispositionOfInvestmentOperatingActivity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Disposition of Investment, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromDispositionOfInvestmentOperatingActivity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromDispositionOfInvestmentOperatingActivity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromDispositionOfInvestmentOperatingActivity" xlink:to="lab_us-gaap_ProceedsFromDispositionOfInvestmentOperatingActivity" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019fd71c-09ae-7b5c-a3fd-4dab6a59ed0f_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetAssetValuePerShare_019fd71c-091c-7624-bedc-6da33d0f433a_terseLabel_en-US" xlink:label="lab_us-gaap_NetAssetValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NET ASSET VALUE PER SHARE (in usd per share)</link:label>
    <link:label id="lab_us-gaap_NetAssetValuePerShare_019fd71c-091c-7b95-967d-ab0ec7bc11e6_periodStartLabel_en-US" xlink:label="lab_us-gaap_NetAssetValuePerShare" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Net asset value, beginning of period (in usd per share)</link:label>
    <link:label id="lab_us-gaap_NetAssetValuePerShare_019fd71c-091c-7b27-a84f-9a15b0b65140_periodEndLabel_en-US" xlink:label="lab_us-gaap_NetAssetValuePerShare" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Net asset value, ending of period (in usd per share)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetAssetValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetAssetValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetAssetValuePerShare" xlink:to="lab_us-gaap_NetAssetValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_019fd71c-0a16-76d1-aae9-d3160b030e94_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_SubscriptionFacilityMember_label_en-US" xlink:label="lab_bxsl_SubscriptionFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subscription Facility [Member]</link:label>
    <link:label id="lab_bxsl_SubscriptionFacilityMember_documentation_en-US" xlink:label="lab_bxsl_SubscriptionFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subscription Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_SubscriptionFacilityMember" xlink:href="bxsl-20260930.xsd#bxsl_SubscriptionFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_SubscriptionFacilityMember" xlink:to="lab_bxsl_SubscriptionFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentInterestRatePaidInKind_019fd71c-09af-7749-92a0-4c14c9feba03_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentInterestRatePaidInKind" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reference rate and spread/paid in kind</link:label>
    <link:label id="lab_us-gaap_InvestmentInterestRatePaidInKind_label_en-US" xlink:label="lab_us-gaap_InvestmentInterestRatePaidInKind" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Interest Rate, Paid in Kind</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentInterestRatePaidInKind" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentInterestRatePaidInKind"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentInterestRatePaidInKind" xlink:to="lab_us-gaap_InvestmentInterestRatePaidInKind" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentCompanyAgreementNumberOfComponents_019fd71c-09af-799b-859a-acb8f46f081b_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentCompanyAgreementNumberOfComponents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of components</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyAgreementNumberOfComponents_label_en-US" xlink:label="lab_bxsl_InvestmentCompanyAgreementNumberOfComponents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Agreement, Number Of Components</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyAgreementNumberOfComponents_documentation_en-US" xlink:label="lab_bxsl_InvestmentCompanyAgreementNumberOfComponents" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Agreement, Number Of Components</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentCompanyAgreementNumberOfComponents" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentCompanyAgreementNumberOfComponents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentCompanyAgreementNumberOfComponents" xlink:to="lab_bxsl_InvestmentCompanyAgreementNumberOfComponents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsMember_019fd71c-091c-7e7c-9900-404266b9f0ab_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsMember_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsMember" xlink:to="lab_us-gaap_CashAndCashEquivalentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_019fd71c-09ae-7325-a911-d179d97f234e_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_ElectricalEquipmentSectorMember_019fd71c-09af-73d0-8cd4-a5909896f934_terseLabel_en-US" xlink:label="lab_bxsl_ElectricalEquipmentSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Electrical Equipment</link:label>
    <link:label id="lab_bxsl_ElectricalEquipmentSectorMember_label_en-US" xlink:label="lab_bxsl_ElectricalEquipmentSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Electrical Equipment Sector [Member]</link:label>
    <link:label id="lab_bxsl_ElectricalEquipmentSectorMember_documentation_en-US" xlink:label="lab_bxsl_ElectricalEquipmentSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Electrical Equipment Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_ElectricalEquipmentSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_ElectricalEquipmentSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_ElectricalEquipmentSectorMember" xlink:to="lab_bxsl_ElectricalEquipmentSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019fd71c-09af-7e2f-9f36-715d9823bb58_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_country_CA_019fd71c-091c-7394-a860-719e8f1946df_terseLabel_en-US" xlink:label="lab_country_CA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Canada</link:label>
    <link:label id="lab_country_CA_label_en-US" xlink:label="lab_country_CA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CANADA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_CA" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_CA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_CA" xlink:to="lab_country_CA" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MaterialHoldingsLLCFirstLienDebt3Member_019fd71c-0a16-7de4-92e1-0fc41f735d43_terseLabel_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLCFirstLienDebt3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC - First Lien Debt</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLCFirstLienDebt3Member_label_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLCFirstLienDebt3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC - First Lien Debt 3 [Member]</link:label>
    <link:label id="lab_bxsl_MaterialHoldingsLLCFirstLienDebt3Member_documentation_en-US" xlink:label="lab_bxsl_MaterialHoldingsLLCFirstLienDebt3Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material Holdings, LLC - First Lien Debt 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MaterialHoldingsLLCFirstLienDebt3Member" xlink:href="bxsl-20260930.xsd#bxsl_MaterialHoldingsLLCFirstLienDebt3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MaterialHoldingsLLCFirstLienDebt3Member" xlink:to="lab_bxsl_MaterialHoldingsLLCFirstLienDebt3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfFairValueHedgesOnResultsOfOperationsAbstract_019fd71c-09af-7f54-96a0-3ad8ce127975_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfFairValueHedgesOnResultsOfOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) from interest rate swaps accounted for as hedges and the related hedged items:</link:label>
    <link:label id="lab_us-gaap_EffectOfFairValueHedgesOnResultsOfOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_EffectOfFairValueHedgesOnResultsOfOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effect of Fair Value Hedges on Results of Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfFairValueHedgesOnResultsOfOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectOfFairValueHedgesOnResultsOfOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectOfFairValueHedgesOnResultsOfOperationsAbstract" xlink:to="lab_us-gaap_EffectOfFairValueHedgesOnResultsOfOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentsAtFairValueMember_019fd71c-091c-7f83-a9a5-bb9573767e95_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments At Fair Value</link:label>
    <link:label id="lab_bxsl_InvestmentsAtFairValueMember_label_en-US" xlink:label="lab_bxsl_InvestmentsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments At Fair Value [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentsAtFairValueMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentsAtFairValueMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentsAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentsAtFairValueMember" xlink:to="lab_bxsl_InvestmentsAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019fd71c-091c-7ba7-b861-e42692b9a3c1_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies (Note 8)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestriction_019fd71c-09af-7d87-a545-4656421551d1_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestriction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contractual sale restrictions</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestriction_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestriction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Equity Security, Contractual Sale Restriction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestriction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestriction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestriction" xlink:to="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestriction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContainerAndPackagingSectorMember_019fd71c-09ae-73b2-9e5e-6dbbca3e0b12_terseLabel_en-US" xlink:label="lab_us-gaap_ContainerAndPackagingSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Containers &amp; Packaging</link:label>
    <link:label id="lab_us-gaap_ContainerAndPackagingSectorMember_label_en-US" xlink:label="lab_us-gaap_ContainerAndPackagingSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Container and Packaging Sector [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContainerAndPackagingSectorMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContainerAndPackagingSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContainerAndPackagingSectorMember" xlink:to="lab_us-gaap_ContainerAndPackagingSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyDividendDistribution_019fd71c-09af-7dfc-8df1-ac16e2ab1a0f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyDividendDistribution" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared and payable from net investment income</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyDividendDistribution_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyDividendDistribution" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Dividend Distribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyDividendDistribution" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyDividendDistribution"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyDividendDistribution" xlink:to="lab_us-gaap_InvestmentCompanyDividendDistribution" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentAdvisoryAgreementMember_019fd71c-09af-7ab3-ac7c-08f2c19d1bea_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentAdvisoryAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Advisory Agreement</link:label>
    <link:label id="lab_bxsl_InvestmentAdvisoryAgreementMember_label_en-US" xlink:label="lab_bxsl_InvestmentAdvisoryAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Advisory Agreement [Member]</link:label>
    <link:label id="lab_bxsl_InvestmentAdvisoryAgreementMember_documentation_en-US" xlink:label="lab_bxsl_InvestmentAdvisoryAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Advisory Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentAdvisoryAgreementMember" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentAdvisoryAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentAdvisoryAgreementMember" xlink:to="lab_bxsl_InvestmentAdvisoryAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_019fd71c-09af-7f3e-a2a2-d6f8d405bf66_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsTable_019fd71c-091c-73a8-87c3-50d14d1f5370_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Table]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsTable_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsTable" xlink:to="lab_us-gaap_OtherCommitmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_country_AU_019fd71c-0a16-72ef-9806-0d811d9bf319_terseLabel_en-US" xlink:label="lab_country_AU" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Australia</link:label>
    <link:label id="lab_country_AU_label_en-US" xlink:label="lab_country_AU" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AUSTRALIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_AU" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_AU"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_AU" xlink:to="lab_country_AU" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium_019fd71c-09af-753c-af87-4853a3cb439f_terseLabel_en-US" xlink:label="lab_bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accretion of discount (amortization of premium)</link:label>
    <link:label id="lab_bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium_label_en-US" xlink:label="lab_bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Accretion Of Discount/Amortization Of Premium</link:label>
    <link:label id="lab_bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium_documentation_en-US" xlink:label="lab_bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Accretion Of Discount/Amortization Of Premium</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium" xlink:href="bxsl-20260930.xsd#bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium" xlink:to="lab_bxsl_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAccretionOfDiscountAmortizationOfPremium" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_019fd71c-09ae-7da7-a4f0-ca6c55035f16_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental information and non-cash activities:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_019fd71c-09ae-775e-be90-1ea205dd11b2_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities and Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:to="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019fd71c-0a16-7fa2-bcbe-23d667431d5d_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentCompanySupplementalDataAbstract_019fd71c-09af-72cd-996f-14dd15e3f257_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentCompanySupplementalDataAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental Data:</link:label>
    <link:label id="lab_bxsl_InvestmentCompanySupplementalDataAbstract_label_en-US" xlink:label="lab_bxsl_InvestmentCompanySupplementalDataAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Supplemental Data [Abstract]</link:label>
    <link:label id="lab_bxsl_InvestmentCompanySupplementalDataAbstract_documentation_en-US" xlink:label="lab_bxsl_InvestmentCompanySupplementalDataAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Supplemental Data</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentCompanySupplementalDataAbstract" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentCompanySupplementalDataAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentCompanySupplementalDataAbstract" xlink:to="lab_bxsl_InvestmentCompanySupplementalDataAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable_019fd71c-0a16-761b-a35c-74510bd2d415_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_019fd71c-09af-700d-8944-7ee2036e0dc3_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend and Interest Income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Securities, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestAndDividendIncomeSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:to="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_New2026NotesMember_019fd71c-09af-75f4-8843-37da6a9fd420_terseLabel_en-US" xlink:label="lab_bxsl_New2026NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New 2026 Notes</link:label>
    <link:label id="lab_bxsl_New2026NotesMember_label_en-US" xlink:label="lab_bxsl_New2026NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New 2026 Notes [Member]</link:label>
    <link:label id="lab_bxsl_New2026NotesMember_documentation_en-US" xlink:label="lab_bxsl_New2026NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New 2026 Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_New2026NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_New2026NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_New2026NotesMember" xlink:to="lab_bxsl_New2026NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsLineItems_019fd71c-09ae-7c29-93a3-ccc96df63baf_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Line Items]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsLineItems_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsLineItems" xlink:to="lab_us-gaap_OtherCommitmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_019fd71c-09ae-7cca-99e5-cc6371888d9b_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Recognition</link:label>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueRecognitionPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:to="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ManagementFeePayable_019fd71c-0a16-7662-bd05-e2f3c71aa468_terseLabel_en-US" xlink:label="lab_us-gaap_ManagementFeePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fees payable (Note 3)</link:label>
    <link:label id="lab_us-gaap_ManagementFeePayable_019fd71c-0a16-76d5-93d6-d0690bb14f0c_verboseLabel_en-US" xlink:label="lab_us-gaap_ManagementFeePayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Management fees payable</link:label>
    <link:label id="lab_us-gaap_ManagementFeePayable_label_en-US" xlink:label="lab_us-gaap_ManagementFeePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fee Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementFeePayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ManagementFeePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ManagementFeePayable" xlink:to="lab_us-gaap_ManagementFeePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TrusteeFees_019fd71c-09ae-7d59-bf3d-c6752bff777e_terseLabel_en-US" xlink:label="lab_us-gaap_TrusteeFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Board of Trustees&#8217; fees</link:label>
    <link:label id="lab_us-gaap_TrusteeFees_label_en-US" xlink:label="lab_us-gaap_TrusteeFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trustee Fees</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TrusteeFees" xlink:to="lab_us-gaap_TrusteeFees" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019fd71c-0a16-7b2f-83b5-9e52a90a3202_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BaseRateMember_019fd71c-09af-716e-9f0b-03e571c23618_terseLabel_en-US" xlink:label="lab_us-gaap_BaseRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Base Rate</link:label>
    <link:label id="lab_us-gaap_BaseRateMember_label_en-US" xlink:label="lab_us-gaap_BaseRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Base Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BaseRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BaseRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BaseRateMember" xlink:to="lab_us-gaap_BaseRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
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    <link:label id="lab_us-gaap_ManagementAndServiceFeesIncentiveRate_019fd71c-091c-78ee-b38f-906aca434e4d_terseLabel_en-US" xlink:label="lab_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Incentive fees rate</link:label>
    <link:label id="lab_us-gaap_ManagementAndServiceFeesIncentiveRate_label_en-US" xlink:label="lab_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management and Service Fees, Incentive Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ManagementAndServiceFeesIncentiveRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:to="lab_us-gaap_ManagementAndServiceFeesIncentiveRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
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    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_019fd71c-0a16-7a0f-8370-473345e23c0e_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_DebtInstrumentAxis_019fd71c-09af-7876-a2b9-29b3045d9666_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTable_019fd71c-0a16-76c9-839b-f10de71cf9c6_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_019fd71c-09af-7499-8bef-05927e02092d_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due to affiliates</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Due to Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInDueToAffiliates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:to="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019fd71c-09ae-7e2a-b0c4-b5599439130e_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings (loss) per share basic (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019fd71c-09ae-7330-9059-4f27edf28dca_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Earnings (loss) per common share basic (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_019fd71c-09af-77e0-94cd-8ad8eca883ed_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeAxis"/>
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    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease"/>
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    <link:label id="lab_bxsl_InvestmentCompanyAgreementTerminationNoticePeriod_019fd71c-09ae-7a30-b19c-6c97c2aad386_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentCompanyAgreementTerminationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notice period</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyAgreementTerminationNoticePeriod_label_en-US" xlink:label="lab_bxsl_InvestmentCompanyAgreementTerminationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Agreement, Termination Notice Period</link:label>
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    <link:label id="lab_bxsl_RelatedPartyTransactionIncomeBasedIncentiveFeeQuarterlyHurdleRate_019fd71c-09af-71a5-82e4-7cfd8322bc3c_terseLabel_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionIncomeBasedIncentiveFeeQuarterlyHurdleRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quarterly hurdle rate</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount_019fd71c-09ae-7629-b8c2-f77dfd75c75b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unused portion</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unused Borrowing Capacity, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount"/>
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    <link:label id="lab_us-gaap_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmount_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Support to Investee Contractually Required, Not Provided, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmount" xlink:to="lab_us-gaap_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_019fd71c-091c-76ba-aa85-5076d575366c_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_CapitalGainsBasedIncentiveFeesRate_019fd71c-09af-7597-8b5e-170a08497c97_terseLabel_en-US" xlink:label="lab_bxsl_CapitalGainsBasedIncentiveFeesRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital gains based incentive rate</link:label>
    <link:label id="lab_bxsl_CapitalGainsBasedIncentiveFeesRate_label_en-US" xlink:label="lab_bxsl_CapitalGainsBasedIncentiveFeesRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Gains Based Incentive Fees, Rate</link:label>
    <link:label id="lab_bxsl_CapitalGainsBasedIncentiveFeesRate_documentation_en-US" xlink:label="lab_bxsl_CapitalGainsBasedIncentiveFeesRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital Gains Based Incentive Fees, Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_CapitalGainsBasedIncentiveFeesRate" xlink:href="bxsl-20260930.xsd#bxsl_CapitalGainsBasedIncentiveFeesRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_CapitalGainsBasedIncentiveFeesRate" xlink:to="lab_bxsl_CapitalGainsBasedIncentiveFeesRate" xlink:type="arc" order="1"/>
    <link:label id="lab_country_GB_01a18a76-4b8a-7651-94ea-c977c4e186c9_terseLabel_en-US" xlink:label="lab_country_GB" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">United Kingdom</link:label>
    <link:label id="lab_country_GB_label_en-US" xlink:label="lab_country_GB" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED KINGDOM</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_GB" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_GB"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_GB" xlink:to="lab_country_GB" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_019fd71c-09ae-7b18-9f57-0572f69a4d50_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeExtensibleEnumeration_019fd71c-09ae-7dd3-91b4-979fbbbdab0d_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Type [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Type [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentTypeExtensibleEnumeration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:to="lab_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019fd71c-09af-78e5-aad0-8cdf85afb8ab_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019fd71c-09af-7af2-90dd-bc37baaa3f4e_verboseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Concentration percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_JacksonHoleFundingFacilityDollarAdvancesMember_019fd71c-09af-7ef6-97de-19b38162961c_terseLabel_en-US" xlink:label="lab_bxsl_JacksonHoleFundingFacilityDollarAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Jackson Hole Funding Facility, Dollar Advances</link:label>
    <link:label id="lab_bxsl_JacksonHoleFundingFacilityDollarAdvancesMember_label_en-US" xlink:label="lab_bxsl_JacksonHoleFundingFacilityDollarAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Jackson Hole Funding Facility, Dollar Advances [Member]</link:label>
    <link:label id="lab_bxsl_JacksonHoleFundingFacilityDollarAdvancesMember_documentation_en-US" xlink:label="lab_bxsl_JacksonHoleFundingFacilityDollarAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Jackson Hole Funding Facility, Dollar Advances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_JacksonHoleFundingFacilityDollarAdvancesMember" xlink:href="bxsl-20260930.xsd#bxsl_JacksonHoleFundingFacilityDollarAdvancesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_JacksonHoleFundingFacilityDollarAdvancesMember" xlink:to="lab_bxsl_JacksonHoleFundingFacilityDollarAdvancesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_VoluntaryWaiverScenarioAxis_019fd71c-09ae-7f4c-95c5-a3000886737a_terseLabel_en-US" xlink:label="lab_bxsl_VoluntaryWaiverScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Voluntary Waiver Scenario [Axis]</link:label>
    <link:label id="lab_bxsl_VoluntaryWaiverScenarioAxis_label_en-US" xlink:label="lab_bxsl_VoluntaryWaiverScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Voluntary Waiver Scenario [Axis]</link:label>
    <link:label id="lab_bxsl_VoluntaryWaiverScenarioAxis_documentation_en-US" xlink:label="lab_bxsl_VoluntaryWaiverScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Voluntary Waiver Scenario</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_VoluntaryWaiverScenarioAxis" xlink:href="bxsl-20260930.xsd#bxsl_VoluntaryWaiverScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_VoluntaryWaiverScenarioAxis" xlink:to="lab_bxsl_VoluntaryWaiverScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_019fd71c-09af-7925-b1ff-a277558b9f14_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesIndustryMember_019fd71c-09ae-7704-bfec-49dbe03c8bb5_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesIndustryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industry Sector [Domain]</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesIndustryMember_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesIndustryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industry Sector [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesIndustryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesIndustryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesIndustryMember" xlink:to="lab_us-gaap_EquitySecuritiesIndustryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedPercentOfNetAssets_019fd71c-09af-7974-8202-6c41bebedaf8_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedPercentOfNetAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as % of Net Assets</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedPercentOfNetAssets_label_en-US" xlink:label="lab_us-gaap_InvestmentOwnedPercentOfNetAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Net Assets, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedPercentOfNetAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentOwnedPercentOfNetAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentOwnedPercentOfNetAssets" xlink:to="lab_us-gaap_InvestmentOwnedPercentOfNetAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A2028NotesMember_019fd71c-09af-754c-8e72-164c1b0f9606_terseLabel_en-US" xlink:label="lab_bxsl_A2028NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028 Notes</link:label>
    <link:label id="lab_bxsl_A2028NotesMember_label_en-US" xlink:label="lab_bxsl_A2028NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2028 Notes [Member]</link:label>
    <link:label id="lab_bxsl_A2028NotesMember_documentation_en-US" xlink:label="lab_bxsl_A2028NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2028 Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A2028NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_A2028NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A2028NotesMember" xlink:to="lab_bxsl_A2028NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_PaymentsOfDebtIssuanceCostsLineOfCreditArrangements_019fd71c-09af-7306-b921-58286d0cb8b1_negatedTerseLabel_en-US" xlink:label="lab_bxsl_PaymentsOfDebtIssuanceCostsLineOfCreditArrangements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deferred financing costs paid</link:label>
    <link:label id="lab_bxsl_PaymentsOfDebtIssuanceCostsLineOfCreditArrangements_label_en-US" xlink:label="lab_bxsl_PaymentsOfDebtIssuanceCostsLineOfCreditArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments Of Debt Issuance Costs, Line Of Credit Arrangements</link:label>
    <link:label id="lab_bxsl_PaymentsOfDebtIssuanceCostsLineOfCreditArrangements_documentation_en-US" xlink:label="lab_bxsl_PaymentsOfDebtIssuanceCostsLineOfCreditArrangements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments Of Debt Issuance Costs, Line Of Credit Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_PaymentsOfDebtIssuanceCostsLineOfCreditArrangements" xlink:href="bxsl-20260930.xsd#bxsl_PaymentsOfDebtIssuanceCostsLineOfCreditArrangements"/>
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    <link:label id="lab_us-gaap_InvestmentCompanyDistributionToShareholdersPerShare_019fd71c-09af-70ae-9e27-24bfbaa0ab09_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyDistributionToShareholdersPerShare" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions from net investment income (in usd per share)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyDistributionToShareholdersPerShare_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyDistributionToShareholdersPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Distribution to Shareholders, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyDistributionToShareholdersPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyDistributionToShareholdersPerShare"/>
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    <link:label id="lab_srt_ShareRepurchaseProgramAxis_019fd71c-09af-7905-af5d-61e48724a506_terseLabel_en-US" xlink:label="lab_srt_ShareRepurchaseProgramAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_ShareRepurchaseProgramAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ShareRepurchaseProgramAxis"/>
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    <link:label id="lab_us-gaap_HedgingDesignationDomain_019fd71c-09af-7701-b848-4550f617e80b_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgingDesignationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationDomain" xlink:to="lab_us-gaap_HedgingDesignationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_MachinerySectorMember_019fd71c-09af-7332-8b3c-572069c48719_terseLabel_en-US" xlink:label="lab_bxsl_MachinerySectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Machinery</link:label>
    <link:label id="lab_bxsl_MachinerySectorMember_label_en-US" xlink:label="lab_bxsl_MachinerySectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Machinery Sector [Member]</link:label>
    <link:label id="lab_bxsl_MachinerySectorMember_documentation_en-US" xlink:label="lab_bxsl_MachinerySectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Machinery Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_MachinerySectorMember" xlink:href="bxsl-20260930.xsd#bxsl_MachinerySectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_MachinerySectorMember" xlink:to="lab_bxsl_MachinerySectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignExchangeForwardMember_019fd71c-091c-7aa8-8dd9-6783229bb964_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignExchangeForwardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency forward contracts</link:label>
    <link:label id="lab_us-gaap_ForeignExchangeForwardMember_label_en-US" xlink:label="lab_us-gaap_ForeignExchangeForwardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Exchange Forward [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignExchangeForwardMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignExchangeForwardMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignExchangeForwardMember" xlink:to="lab_us-gaap_ForeignExchangeForwardMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentPolicyTextBlock_019fd71c-09af-7e84-a06f-baf0a2f087f3_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments/Receivables/Payables From Investments Sold/Purchased</link:label>
    <link:label id="lab_us-gaap_InvestmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentPolicyTextBlock" xlink:to="lab_us-gaap_InvestmentPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_UnsecuredDebtUnrealizedGainLossMember_019fd71c-09af-7be6-9c40-0c52fa4a147e_terseLabel_en-US" xlink:label="lab_bxsl_UnsecuredDebtUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_bxsl_UnsecuredDebtUnrealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_UnsecuredDebtUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Unrealized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_UnsecuredDebtUnrealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_UnsecuredDebtUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_UnsecuredDebtUnrealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_UnsecuredDebtUnrealizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_UnsecuredDebtUnrealizedGainLossMember" xlink:to="lab_bxsl_UnsecuredDebtUnrealizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_BXSL20251FacilityMember_019fd71c-09af-7aea-b95a-f13c10cf0bf8_terseLabel_en-US" xlink:label="lab_bxsl_BXSL20251FacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BXSL 2025-1 Facility</link:label>
    <link:label id="lab_bxsl_BXSL20251FacilityMember_label_en-US" xlink:label="lab_bxsl_BXSL20251FacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BXSL 2025-1 Facility [Member]</link:label>
    <link:label id="lab_bxsl_BXSL20251FacilityMember_documentation_en-US" xlink:label="lab_bxsl_BXSL20251FacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BXSL 2025-1 Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_BXSL20251FacilityMember" xlink:href="bxsl-20260930.xsd#bxsl_BXSL20251FacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_BXSL20251FacilityMember" xlink:to="lab_bxsl_BXSL20251FacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_HealthCareProvidersServicesSectorMember_019fd71c-09af-7079-948b-0774c323b4cf_terseLabel_en-US" xlink:label="lab_bxsl_HealthCareProvidersServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Health Care Providers &amp; Services</link:label>
    <link:label id="lab_bxsl_HealthCareProvidersServicesSectorMember_label_en-US" xlink:label="lab_bxsl_HealthCareProvidersServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Health Care Providers &amp; Services Sector [Member]</link:label>
    <link:label id="lab_bxsl_HealthCareProvidersServicesSectorMember_documentation_en-US" xlink:label="lab_bxsl_HealthCareProvidersServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Health Care Providers &amp; Services Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_HealthCareProvidersServicesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_HealthCareProvidersServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_HealthCareProvidersServicesSectorMember" xlink:to="lab_bxsl_HealthCareProvidersServicesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_LineOfCreditFacilityUnusedCapacityPercentage_019fd71c-0a16-7320-aa4c-82d86160c538_terseLabel_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityUnusedCapacityPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unused capacity percentage</link:label>
    <link:label id="lab_bxsl_LineOfCreditFacilityUnusedCapacityPercentage_label_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityUnusedCapacityPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Unused Capacity, Percentage</link:label>
    <link:label id="lab_bxsl_LineOfCreditFacilityUnusedCapacityPercentage_documentation_en-US" xlink:label="lab_bxsl_LineOfCreditFacilityUnusedCapacityPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Unused Capacity, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_LineOfCreditFacilityUnusedCapacityPercentage" xlink:href="bxsl-20260930.xsd#bxsl_LineOfCreditFacilityUnusedCapacityPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_LineOfCreditFacilityUnusedCapacityPercentage" xlink:to="lab_bxsl_LineOfCreditFacilityUnusedCapacityPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019fd71c-09ae-71bd-a6b8-86792ad47bfb_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsAxis_01a198ab-4d87-7bff-b33f-11fde8e86b0b_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends [Axis]</link:label>
    <link:label id="lab_us-gaap_DividendsAxis_label_en-US" xlink:label="lab_us-gaap_DividendsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsAxis" xlink:to="lab_us-gaap_DividendsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_019fd71c-09ae-7329-98f0-1c6247007ce3_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Offsetting Liabilities</link:label>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_June2030NotesMember_019fd71c-09af-75d7-b274-9931ed9182f7_terseLabel_en-US" xlink:label="lab_bxsl_June2030NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">June 2030 Notes</link:label>
    <link:label id="lab_bxsl_June2030NotesMember_label_en-US" xlink:label="lab_bxsl_June2030NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">June 2030 Notes [Member]</link:label>
    <link:label id="lab_bxsl_June2030NotesMember_documentation_en-US" xlink:label="lab_bxsl_June2030NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">June 2030 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_June2030NotesMember" xlink:href="bxsl-20260930.xsd#bxsl_June2030NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_June2030NotesMember" xlink:to="lab_bxsl_June2030NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue_019fd71c-09af-7ff0-88c1-6ff09c3bfc45_negatedTerseLabel_en-US" xlink:label="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue_label_en-US" xlink:label="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Commitment to Investee, Future Amount, Fair Value</link:label>
    <link:label id="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue_documentation_en-US" xlink:label="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Commitment to Investee, Future Amount, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue" xlink:to="lab_bxsl_InvestmentCompanyFinancialCommitmentToInvesteeFutureAmountFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_RelatedPartyTransactionInitialTerm_019fd71c-09ae-7fc9-a1a4-831c094b5070_terseLabel_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionInitialTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, initial term</link:label>
    <link:label id="lab_bxsl_RelatedPartyTransactionInitialTerm_label_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionInitialTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Initial Term</link:label>
    <link:label id="lab_bxsl_RelatedPartyTransactionInitialTerm_documentation_en-US" xlink:label="lab_bxsl_RelatedPartyTransactionInitialTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Initial Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_RelatedPartyTransactionInitialTerm" xlink:href="bxsl-20260930.xsd#bxsl_RelatedPartyTransactionInitialTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_RelatedPartyTransactionInitialTerm" xlink:to="lab_bxsl_RelatedPartyTransactionInitialTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_019fd71c-09ae-7df7-b2bf-8d11644e0e16_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NondesignatedMember_019fd71c-09af-7678-96fa-8b8e11cbafb6_terseLabel_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Not Designated as Hedging Instrument</link:label>
    <link:label id="lab_us-gaap_NondesignatedMember_label_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Not Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NondesignatedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NondesignatedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NondesignatedMember" xlink:to="lab_us-gaap_NondesignatedMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Still Held, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossInvestmentIncomeOperating_019fd71c-09ae-751d-be4d-9e8a52f3a198_totalLabel_en-US" xlink:label="lab_us-gaap_GrossInvestmentIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total investment income</link:label>
    <link:label id="lab_us-gaap_GrossInvestmentIncomeOperating_label_en-US" xlink:label="lab_us-gaap_GrossInvestmentIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Investment Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossInvestmentIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GrossInvestmentIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossInvestmentIncomeOperating" xlink:to="lab_us-gaap_GrossInvestmentIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019fd71c-0a16-7d64-a791-f607774b3c00_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Derivative liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_VoluntaryWaiverNotInPlaceMember_019fd71c-09ae-74d7-9c5c-db0dd9d46db7_terseLabel_en-US" xlink:label="lab_bxsl_VoluntaryWaiverNotInPlaceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Voluntary Waiver Not In Place</link:label>
    <link:label id="lab_bxsl_VoluntaryWaiverNotInPlaceMember_label_en-US" xlink:label="lab_bxsl_VoluntaryWaiverNotInPlaceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Voluntary Waiver Not In Place [Member]</link:label>
    <link:label id="lab_bxsl_VoluntaryWaiverNotInPlaceMember_documentation_en-US" xlink:label="lab_bxsl_VoluntaryWaiverNotInPlaceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Voluntary Waiver Not In Place</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_VoluntaryWaiverNotInPlaceMember" xlink:href="bxsl-20260930.xsd#bxsl_VoluntaryWaiverNotInPlaceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_VoluntaryWaiverNotInPlaceMember" xlink:to="lab_bxsl_VoluntaryWaiverNotInPlaceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_EnergyEquipmentServicesSectorMember_019fd71c-09ae-7686-bd03-eca54160875e_terseLabel_en-US" xlink:label="lab_bxsl_EnergyEquipmentServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Energy Equipment &amp; Services</link:label>
    <link:label id="lab_bxsl_EnergyEquipmentServicesSectorMember_label_en-US" xlink:label="lab_bxsl_EnergyEquipmentServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Energy Equipment &amp; Services Sector [Member]</link:label>
    <link:label id="lab_bxsl_EnergyEquipmentServicesSectorMember_documentation_en-US" xlink:label="lab_bxsl_EnergyEquipmentServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Energy Equipment &amp; Services Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_EnergyEquipmentServicesSectorMember" xlink:href="bxsl-20260930.xsd#bxsl_EnergyEquipmentServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_EnergyEquipmentServicesSectorMember" xlink:to="lab_bxsl_EnergyEquipmentServicesSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_019fd71c-09af-7cc3-bd92-67c8b3360732_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign Currency Transactions</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:to="lab_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019fd71c-09ae-72ec-9c3e-1d133723b269_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_EquitySecuritiesUnrealizedGainLossMember_019fd71c-09ae-71a6-80b0-ba1fd7be79fe_terseLabel_en-US" xlink:label="lab_bxsl_EquitySecuritiesUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Securities, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_bxsl_EquitySecuritiesUnrealizedGainLossMember_label_en-US" xlink:label="lab_bxsl_EquitySecuritiesUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, Unrealized Gain (Loss) [Member]</link:label>
    <link:label id="lab_bxsl_EquitySecuritiesUnrealizedGainLossMember_documentation_en-US" xlink:label="lab_bxsl_EquitySecuritiesUnrealizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_EquitySecuritiesUnrealizedGainLossMember" xlink:href="bxsl-20260930.xsd#bxsl_EquitySecuritiesUnrealizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_EquitySecuritiesUnrealizedGainLossMember" xlink:to="lab_bxsl_EquitySecuritiesUnrealizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueRollForward_019fd71c-0a16-70e3-971c-2c3c0e648112_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments in and Advances to Affiliates, at Fair Value [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueRollForward_label_en-US" xlink:label="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in and Advances to Affiliates, at Fair Value [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueRollForward" xlink:to="lab_us-gaap_InvestmentsInAndAdvancesToAffiliatesAtFairValueRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember_019fd71c-09af-7e57-b8ea-afb47bf3c7df_terseLabel_en-US" xlink:label="lab_bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class A-L Loans, Senior Secured Floating Rate</link:label>
    <link:label id="lab_bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember_label_en-US" xlink:label="lab_bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class A-L Loans, Senior Secured Floating Rate [Member]</link:label>
    <link:label id="lab_bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember_documentation_en-US" xlink:label="lab_bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024-1 CLO, Class A-L Loans, Senior Secured Floating Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember" xlink:href="bxsl-20260930.xsd#bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember" xlink:to="lab_bxsl_A20241CLOClassALLoansSeniorSecuredFloatingRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingBeforeTax_019fd71c-09ae-748b-b189-74e9315864fb_verboseLabel_en-US" xlink:label="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingBeforeTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net Realized Gain (Loss)</link:label>
    <link:label id="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingBeforeTax_label_en-US" xlink:label="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss), Investment, Derivative, and Foreign Currency Transaction Price Change, Operating, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingBeforeTax" xlink:to="lab_us-gaap_RealizedGainLossInvestmentDerivativeAndForeignCurrencyTransactionPriceChangeOperatingBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019fd71c-0a16-74e5-bf2c-28752548ce5d_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyPortfolioTurnover_019fd71c-09af-7fbd-acea-15831431c4ee_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyPortfolioTurnover" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portfolio turnover rate</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyPortfolioTurnover_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyPortfolioTurnover" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Portfolio Turnover</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyPortfolioTurnover" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyPortfolioTurnover"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyPortfolioTurnover" xlink:to="lab_us-gaap_InvestmentCompanyPortfolioTurnover" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_WellsFargoBankMember_019fd71c-09ae-7344-8c1c-270824d26ab7_terseLabel_en-US" xlink:label="lab_bxsl_WellsFargoBankMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Wells Fargo Bank, N.A.</link:label>
    <link:label id="lab_bxsl_WellsFargoBankMember_label_en-US" xlink:label="lab_bxsl_WellsFargoBankMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Wells Fargo Bank [Member]</link:label>
    <link:label id="lab_bxsl_WellsFargoBankMember_documentation_en-US" xlink:label="lab_bxsl_WellsFargoBankMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Wells Fargo Bank</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_WellsFargoBankMember" xlink:href="bxsl-20260930.xsd#bxsl_WellsFargoBankMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_WellsFargoBankMember" xlink:to="lab_bxsl_WellsFargoBankMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnamortizedDebtIssuanceExpense_019fd71c-09af-7fbe-a5da-f52b52a0aabe_terseLabel_en-US" xlink:label="lab_us-gaap_UnamortizedDebtIssuanceExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unamortized Debt Issuance Costs (including premiums and discounts)</link:label>
    <link:label id="lab_us-gaap_UnamortizedDebtIssuanceExpense_label_en-US" xlink:label="lab_us-gaap_UnamortizedDebtIssuanceExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unamortized Debt Issuance Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnamortizedDebtIssuanceExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnamortizedDebtIssuanceExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnamortizedDebtIssuanceExpense" xlink:to="lab_us-gaap_UnamortizedDebtIssuanceExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019fd71c-09af-745e-89ce-48af3461709c_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestrictionRemainingPeriod_019fd71c-09af-77be-a3e0-545102b23114_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestrictionRemainingPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contractual sale restriction, remaining period</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestrictionRemainingPeriod_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestrictionRemainingPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Equity Security, Contractual Sale Restriction, Remaining Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestrictionRemainingPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestrictionRemainingPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestrictionRemainingPeriod" xlink:to="lab_us-gaap_InvestmentCompanyEquitySecurityFvNiContractualSaleRestrictionRemainingPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_019fd71c-0a16-708c-9a19-96b5d41e0732_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_bxsl_InvestmentPercentageOfPortfolioAboveFloorRate_019fd71c-09af-73c0-9e5f-563ffa6c5224_terseLabel_en-US" xlink:label="lab_bxsl_InvestmentPercentageOfPortfolioAboveFloorRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of portfolio above floor rate</link:label>
    <link:label id="lab_bxsl_InvestmentPercentageOfPortfolioAboveFloorRate_label_en-US" xlink:label="lab_bxsl_InvestmentPercentageOfPortfolioAboveFloorRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Percentage Of Portfolio Above Floor Rate</link:label>
    <link:label id="lab_bxsl_InvestmentPercentageOfPortfolioAboveFloorRate_documentation_en-US" xlink:label="lab_bxsl_InvestmentPercentageOfPortfolioAboveFloorRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment, Percentage Of Portfolio Above Floor Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bxsl_InvestmentPercentageOfPortfolioAboveFloorRate" xlink:href="bxsl-20260930.xsd#bxsl_InvestmentPercentageOfPortfolioAboveFloorRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bxsl_InvestmentPercentageOfPortfolioAboveFloorRate" xlink:to="lab_bxsl_InvestmentPercentageOfPortfolioAboveFloorRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems_019fd71c-091c-744f-b499-ae2c43b1b3a6_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Line Items]</link:label>
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