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  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTotalLabel"/>
  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_InvestmentCompanyInvestmentIncomeLossFromCapitalActivityPerShare_019e83f7-3513-7de3-9806-4fe24e63c4c6_totalLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyInvestmentIncomeLossFromCapitalActivityPerShare" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Increase in Net Assets Resulting from Capital Activity (in USD per unit)</link:label>
    <link:label id="lab_bpef_InvestmentCompanyInvestmentIncomeLossFromCapitalActivityPerShare_label_en-US" xlink:label="lab_bpef_InvestmentCompanyInvestmentIncomeLossFromCapitalActivityPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Investment Income (Loss) From Capital Activity, Per Share</link:label>
    <link:label id="lab_bpef_InvestmentCompanyInvestmentIncomeLossFromCapitalActivityPerShare_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyInvestmentIncomeLossFromCapitalActivityPerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Investment Income (Loss) From Capital Activity, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyInvestmentIncomeLossFromCapitalActivityPerShare" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyInvestmentIncomeLossFromCapitalActivityPerShare"/>
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    <link:label id="lab_bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod_019e83f7-35de-74ef-b565-785abdf73225_terseLabel_en-US" xlink:label="lab_bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reimbursement period (in months)</link:label>
    <link:label id="lab_bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod_label_en-US" xlink:label="lab_bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Related Parties, Reimbursement Period</link:label>
    <link:label id="lab_bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod_documentation_en-US" xlink:label="lab_bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Liabilities, Related Parties, Reimbursement Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod" xlink:href="bpef-20260630.xsd#bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod" xlink:to="lab_bpef_OtherLiabilitiesRelatedPartiesReimbursementPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019e83f7-3514-7f45-b2e4-a9015b794d1f_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <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"/>
    <link:label id="lab_bpef_IndustrialsSectorMember_019e83f7-3513-7f4b-82d0-a6e5ce3e4c6e_terseLabel_en-US" xlink:label="lab_bpef_IndustrialsSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industrials</link:label>
    <link:label id="lab_bpef_IndustrialsSectorMember_label_en-US" xlink:label="lab_bpef_IndustrialsSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industrials Sector [Member]</link:label>
    <link:label id="lab_bpef_IndustrialsSectorMember_documentation_en-US" xlink:label="lab_bpef_IndustrialsSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Industrials Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_IndustrialsSectorMember" xlink:href="bpef-20260630.xsd#bpef_IndustrialsSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_IndustrialsSectorMember" xlink:to="lab_bpef_IndustrialsSectorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019e83f7-3513-7be6-bb7b-f9e11f55da33_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_bpef_ManagementFeesWaivedPolicyTextBlock_019e83f7-3513-79f6-9b66-cf079a976b2c_terseLabel_en-US" xlink:label="lab_bpef_ManagementFeesWaivedPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management Fees Waived</link:label>
    <link:label id="lab_bpef_ManagementFeesWaivedPolicyTextBlock_label_en-US" xlink:label="lab_bpef_ManagementFeesWaivedPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fees Waived [Policy Text Block]</link:label>
    <link:label id="lab_bpef_ManagementFeesWaivedPolicyTextBlock_documentation_en-US" xlink:label="lab_bpef_ManagementFeesWaivedPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management Fees Waived</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ManagementFeesWaivedPolicyTextBlock" xlink:href="bpef-20260630.xsd#bpef_ManagementFeesWaivedPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ManagementFeesWaivedPolicyTextBlock" xlink:to="lab_bpef_ManagementFeesWaivedPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_InvestmentOwnedNetAssetsTargetPercentage_019e83f7-3513-787c-a6e9-a10f88a41ec5_terseLabel_en-US" xlink:label="lab_bpef_InvestmentOwnedNetAssetsTargetPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Target percentage of investments in net assets</link:label>
    <link:label id="lab_bpef_InvestmentOwnedNetAssetsTargetPercentage_label_en-US" xlink:label="lab_bpef_InvestmentOwnedNetAssetsTargetPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Net Assets, Target Percentage</link:label>
    <link:label id="lab_bpef_InvestmentOwnedNetAssetsTargetPercentage_documentation_en-US" xlink:label="lab_bpef_InvestmentOwnedNetAssetsTargetPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Owned, Net Assets, Target Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentOwnedNetAssetsTargetPercentage" xlink:href="bpef-20260630.xsd#bpef_InvestmentOwnedNetAssetsTargetPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentOwnedNetAssetsTargetPercentage" xlink:to="lab_bpef_InvestmentOwnedNetAssetsTargetPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019e83f7-3513-75f0-9833-8b5914ab9bf8_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:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" 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_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_019e83f7-3513-7d85-b451-629e1c085ba7_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_us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_019e83f7-3513-7b59-8f00-cff0bda22223_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 Funds Investments by Fair Value Hierarchy Levels</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_InterestExpense_019e83f7-3513-7544-bf12-c630e63f9c2e_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_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_bpef_DerivativeAssetNetAssetsPercentage_019e83f7-3514-772f-98d9-64b1e959223b_terseLabel_en-US" xlink:label="lab_bpef_DerivativeAssetNetAssetsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as a Percentage of Net Assets, Derivative Instrument</link:label>
    <link:label id="lab_bpef_DerivativeAssetNetAssetsPercentage_label_en-US" xlink:label="lab_bpef_DerivativeAssetNetAssetsPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Net Assets, Percentage</link:label>
    <link:label id="lab_bpef_DerivativeAssetNetAssetsPercentage_documentation_en-US" xlink:label="lab_bpef_DerivativeAssetNetAssetsPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Asset, Net Assets, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_DerivativeAssetNetAssetsPercentage" xlink:href="bpef-20260630.xsd#bpef_DerivativeAssetNetAssetsPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_DerivativeAssetNetAssetsPercentage" xlink:to="lab_bpef_DerivativeAssetNetAssetsPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityExTransitionPeriod_019e83f7-3514-7a47-8ad5-431a124e8c46_terseLabel_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:label id="lab_dei_EntityExTransitionPeriod_label_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityExTransitionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityExTransitionPeriod" xlink:to="lab_dei_EntityExTransitionPeriod" 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_InvestmentManagementAgreementMember_019e83f7-35de-73c8-9ed3-0acf941fbbe3_terseLabel_en-US" xlink:label="lab_bpef_InvestmentManagementAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Management Agreement</link:label>
    <link:label id="lab_bpef_InvestmentManagementAgreementMember_label_en-US" xlink:label="lab_bpef_InvestmentManagementAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Management Agreement [Member]</link:label>
    <link:label id="lab_bpef_InvestmentManagementAgreementMember_documentation_en-US" xlink:label="lab_bpef_InvestmentManagementAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Management Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentManagementAgreementMember" xlink:href="bpef-20260630.xsd#bpef_InvestmentManagementAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentManagementAgreementMember" xlink:to="lab_bpef_InvestmentManagementAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_019e83f7-3513-7939-8cd3-e176b814c0c1_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_bpef_CashNetAssetsPercentage_019e83f7-3513-7350-a8c3-6235fc7f102e_terseLabel_en-US" xlink:label="lab_bpef_CashNetAssetsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as a Percentage of Net Assets, Cash</link:label>
    <link:label id="lab_bpef_CashNetAssetsPercentage_label_en-US" xlink:label="lab_bpef_CashNetAssetsPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Net Assets, Percentage</link:label>
    <link:label id="lab_bpef_CashNetAssetsPercentage_documentation_en-US" xlink:label="lab_bpef_CashNetAssetsPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash, Net Assets, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_CashNetAssetsPercentage" xlink:href="bpef-20260630.xsd#bpef_CashNetAssetsPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_CashNetAssetsPercentage" xlink:to="lab_bpef_CashNetAssetsPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019e83f7-3514-7dc9-b8fb-5dd89bd0d2e8_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:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" 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_bpef_RedemptionDiscountPayableToAffiliates_019e83f7-3514-76f0-8017-46fcb2ff34af_terseLabel_en-US" xlink:label="lab_bpef_RedemptionDiscountPayableToAffiliates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class B-1 Redemption Discount Payable</link:label>
    <link:label id="lab_bpef_RedemptionDiscountPayableToAffiliates_label_en-US" xlink:label="lab_bpef_RedemptionDiscountPayableToAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redemption Discount Payable To Affiliates</link:label>
    <link:label id="lab_bpef_RedemptionDiscountPayableToAffiliates_documentation_en-US" xlink:label="lab_bpef_RedemptionDiscountPayableToAffiliates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redemption Discount Payable To Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_RedemptionDiscountPayableToAffiliates" xlink:href="bpef-20260630.xsd#bpef_RedemptionDiscountPayableToAffiliates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_RedemptionDiscountPayableToAffiliates" xlink:to="lab_bpef_RedemptionDiscountPayableToAffiliates" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019e83f7-35de-799c-adac-0f0b40a440bc_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:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" 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_us-gaap_NetInvestmentIncome_019e83f7-3513-77bb-89ca-2a7fa5a038b4_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 (Loss) Before Income 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_us-gaap_InvestmentTypeCategorizationMember_019e83f7-3514-7cc8-8de6-554559453c48_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_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019e83f7-3513-765e-8ef2-f4237cd28fd9_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">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_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_bpef_PaymentOfRedemptionsToAffiliates_019e83f7-3513-7653-94f2-d2873a0a362f_negatedTerseLabel_en-US" xlink:label="lab_bpef_PaymentOfRedemptionsToAffiliates" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments of Class B-1 Redemptions to Affiliates</link:label>
    <link:label id="lab_bpef_PaymentOfRedemptionsToAffiliates_019e83f7-3513-7f2e-95f2-96981132cc83_terseLabel_en-US" xlink:label="lab_bpef_PaymentOfRedemptionsToAffiliates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption payments</link:label>
    <link:label id="lab_bpef_PaymentOfRedemptionsToAffiliates_label_en-US" xlink:label="lab_bpef_PaymentOfRedemptionsToAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment Of Redemptions To Affiliates</link:label>
    <link:label id="lab_bpef_PaymentOfRedemptionsToAffiliates_documentation_en-US" xlink:label="lab_bpef_PaymentOfRedemptionsToAffiliates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payment Of Redemptions To Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PaymentOfRedemptionsToAffiliates" xlink:href="bpef-20260630.xsd#bpef_PaymentOfRedemptionsToAffiliates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PaymentOfRedemptionsToAffiliates" xlink:to="lab_bpef_PaymentOfRedemptionsToAffiliates" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019e83f7-3513-704d-8a0e-92234e707a50_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:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" 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_us-gaap_PartnersCapitalAccountUnitsContributed_019e83f7-3513-7c9a-b1b7-d85c857d5ecf_verboseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountUnitsContributed" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Units Issued (in units)</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountUnitsContributed_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountUnitsContributed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partners' Capital Account, Units, Contributed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnersCapitalAccountUnitsContributed" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountUnitsContributed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnersCapitalAccountUnitsContributed" xlink:to="lab_us-gaap_PartnersCapitalAccountUnitsContributed" 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_bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements_019e83f7-3514-74aa-bb26-a8aee85de85c_totalLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Expenses after fees waived (as percent)</link:label>
    <link:label id="lab_bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements_label_en-US" xlink:label="lab_bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Expense Ratio After Fee Waiver And Reimbursements</link:label>
    <link:label id="lab_bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Expense Ratio After Fee Waiver And Reimbursements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements" xlink:to="lab_bpef_InvestmentCompanyExpenseRatioAfterFeeWaiverAndReimbursements" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock_019e83f7-3514-7e6d-a41d-ddd6d2301afa_terseLabel_en-US" xlink:label="lab_bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption of Class B-1 Units</link:label>
    <link:label id="lab_bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock_label_en-US" xlink:label="lab_bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redemption Of Partners' Capital Account [Policy Text Block]</link:label>
    <link:label id="lab_bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock_documentation_en-US" xlink:label="lab_bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redemption Of Partners' Capital Account</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock" xlink:href="bpef-20260630.xsd#bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock" xlink:to="lab_bpef_RedemptionOfPartnersCapitalAccountPolicyTextBlock" 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_bpef_ManagementFeeWaiverPeriod_019e83f7-3514-73f9-af88-75b47f75bf0b_terseLabel_en-US" xlink:label="lab_bpef_ManagementFeeWaiverPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management fee, waiver period</link:label>
    <link:label id="lab_bpef_ManagementFeeWaiverPeriod_label_en-US" xlink:label="lab_bpef_ManagementFeeWaiverPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fee, Waiver Period</link:label>
    <link:label id="lab_bpef_ManagementFeeWaiverPeriod_documentation_en-US" xlink:label="lab_bpef_ManagementFeeWaiverPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management Fee, Waiver Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ManagementFeeWaiverPeriod" xlink:href="bpef-20260630.xsd#bpef_ManagementFeeWaiverPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ManagementFeeWaiverPeriod" xlink:to="lab_bpef_ManagementFeeWaiverPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019fce8a-2c79-7748-a3e1-9c52270950d4_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" 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_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_019e83f7-3513-7abd-8ae1-a83b7ea1ccab_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 Aggregate Notional Amount and Fair Value 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_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_019e83f7-3513-7742-b8f1-a52c4029d51d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Decrease (Increase) in Interest Receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Interest Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_ServicingFeesPayable_019e83f7-3513-7a49-9aad-7ef01a9e5d7c_terseLabel_en-US" xlink:label="lab_bpef_ServicingFeesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Fees Payable</link:label>
    <link:label id="lab_bpef_ServicingFeesPayable_019e83f7-3513-7984-9643-7cae4b0083f2_verboseLabel_en-US" xlink:label="lab_bpef_ServicingFeesPayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Servicing fees payable</link:label>
    <link:label id="lab_bpef_ServicingFeesPayable_label_en-US" xlink:label="lab_bpef_ServicingFeesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Fees Payable</link:label>
    <link:label id="lab_bpef_ServicingFeesPayable_documentation_en-US" xlink:label="lab_bpef_ServicingFeesPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Servicing Fees Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ServicingFeesPayable" xlink:href="bpef-20260630.xsd#bpef_ServicingFeesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ServicingFeesPayable" xlink:to="lab_bpef_ServicingFeesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum_019e83f7-3513-7eec-89e0-28fde43d2d18_terseLabel_en-US" xlink:label="lab_bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of management fee payment of net asset value per annum</link:label>
    <link:label id="lab_bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum_label_en-US" xlink:label="lab_bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Of Management Fee Payment Of Net Asset Value Per Annum</link:label>
    <link:label id="lab_bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum_documentation_en-US" xlink:label="lab_bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percentage Of Management Fee Payment Of Net Asset Value Per Annum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum" xlink:href="bpef-20260630.xsd#bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum" xlink:to="lab_bpef_PercentageOfManagementFeePaymentOfNetAssetValuePerAnnum" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019e83f7-3513-7c1f-be49-a6361a44a5ee_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:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" 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_PartnersCapitalAccountUnitsSaleOfUnits_019fd8f9-bc47-7967-863e-7cc57a5f7f51_terseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountUnitsSaleOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Units issued</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountUnitsSaleOfUnits_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountUnitsSaleOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partners' Capital Account, Units, Sale of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnersCapitalAccountUnitsSaleOfUnits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountUnitsSaleOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnersCapitalAccountUnitsSaleOfUnits" xlink:to="lab_us-gaap_PartnersCapitalAccountUnitsSaleOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_InvestmentsCashAndDerivativeAssetsFairValue_019e83f7-3513-7ce8-81e8-62a836c64b8b_totalLabel_en-US" xlink:label="lab_bpef_InvestmentsCashAndDerivativeAssetsFairValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Investments, Cash and Derivative Instruments</link:label>
    <link:label id="lab_bpef_InvestmentsCashAndDerivativeAssetsFairValue_label_en-US" xlink:label="lab_bpef_InvestmentsCashAndDerivativeAssetsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Cash, And Derivative Assets, Fair Value</link:label>
    <link:label id="lab_bpef_InvestmentsCashAndDerivativeAssetsFairValue_documentation_en-US" xlink:label="lab_bpef_InvestmentsCashAndDerivativeAssetsFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Cash, And Derivative Assets, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentsCashAndDerivativeAssetsFairValue" xlink:href="bpef-20260630.xsd#bpef_InvestmentsCashAndDerivativeAssetsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentsCashAndDerivativeAssetsFairValue" xlink:to="lab_bpef_InvestmentsCashAndDerivativeAssetsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TaxesPayableCurrentAndNoncurrent_019e83f7-35de-7733-8b5d-eefc8cf36dbb_terseLabel_en-US" xlink:label="lab_us-gaap_TaxesPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Payable</link:label>
    <link:label id="lab_us-gaap_TaxesPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_TaxesPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Taxes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxesPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TaxesPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TaxesPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_TaxesPayableCurrentAndNoncurrent" 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_dei_DocumentInformationLineItems_019e83f7-3514-7ca0-a1f5-1f3a07ec058c_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019e83f7-3514-799a-900a-4699bd050782_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_us-gaap_StatementClassOfStockAxis_019e83f7-3513-7b0d-9d7e-2fc99135480e_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable_019e83f7-3514-7396-a359-7cb9f6a99cbb_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum percentage of shares redeemable</link:label>
    <link:label id="lab_bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable_label_en-US" xlink:label="lab_bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Maximum Percentage Of Shares Redeemable</link:label>
    <link:label id="lab_bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maximum Percentage Of Shares Redeemable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable" xlink:to="lab_bpef_InvestmentCompanyMaximumPercentageOfSharesRedeemable" 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_us-gaap_PartnersCapitalAccountRedemptions_019e83f7-3513-7068-9f51-5ac34890417c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountRedemptions" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Redemption of Units</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountRedemptions_019e83f7-3513-74a4-89b3-7ba1d5aa743f_netLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountRedemptions" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Redemptions of units</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountRedemptions_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountRedemptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partners' Capital Account, Redemptions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnersCapitalAccountRedemptions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountRedemptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnersCapitalAccountRedemptions" xlink:to="lab_us-gaap_PartnersCapitalAccountRedemptions" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_AdministrationFeesMember_019e83f7-3513-707e-9708-9fc2ffcbf3e5_terseLabel_en-US" xlink:label="lab_bpef_AdministrationFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administration Fees</link:label>
    <link:label id="lab_bpef_AdministrationFeesMember_label_en-US" xlink:label="lab_bpef_AdministrationFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administration Fees [Member]</link:label>
    <link:label id="lab_bpef_AdministrationFeesMember_documentation_en-US" xlink:label="lab_bpef_AdministrationFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Administration Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_AdministrationFeesMember" xlink:href="bpef-20260630.xsd#bpef_AdministrationFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_AdministrationFeesMember" xlink:to="lab_bpef_AdministrationFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalUnitClassDomain_019e83f7-3513-7431-ba43-67b688fc4f65_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalUnitClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital Unit, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_CapitalUnitClassDomain_label_en-US" xlink:label="lab_us-gaap_CapitalUnitClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Unit, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalUnitClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CapitalUnitClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalUnitClassDomain" xlink:to="lab_us-gaap_CapitalUnitClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019e83f7-3513-7040-880c-9e324d1eaba4_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 II</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"/>
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    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossPerShare_019e83f7-3514-7cec-9004-f339619bc89c_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 (Loss) (in USD per unit)</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"/>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019e83f7-3513-76de-a940-6e82802ccfd4_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">Aggregate amount</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"/>
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    <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>
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    <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"/>
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    <link:label id="lab_bpef_ValuationTechniqueCostPlusAccruedInterestMember_label_en-US" xlink:label="lab_bpef_ValuationTechniqueCostPlusAccruedInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Cost Plus Accrued Interest [Member]</link:label>
    <link:label id="lab_bpef_ValuationTechniqueCostPlusAccruedInterestMember_documentation_en-US" xlink:label="lab_bpef_ValuationTechniqueCostPlusAccruedInterestMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Cost Plus Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ValuationTechniqueCostPlusAccruedInterestMember" xlink:href="bpef-20260630.xsd#bpef_ValuationTechniqueCostPlusAccruedInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ValuationTechniqueCostPlusAccruedInterestMember" xlink:to="lab_bpef_ValuationTechniqueCostPlusAccruedInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyNetAssetValuePerSharePeriodIncreaseDecrease_019e83f7-3513-7a67-a139-4e3e9cf0d109_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">Net Increase (Decrease) in Net Assets (in USD per unit)</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_OtherExpenses_019e83f7-3514-7ff4-b0fa-d9e116e29070_terseLabel_en-US" xlink:label="lab_us-gaap_OtherExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Expenses</link:label>
    <link:label id="lab_us-gaap_OtherExpenses_label_en-US" xlink:label="lab_us-gaap_OtherExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherExpenses" xlink:to="lab_us-gaap_OtherExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_019e83f7-3513-75d8-bc6a-b3bd79cbcfba_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</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"/>
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    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019e83f7-3513-77cc-836c-d9f43ac2b55a_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"/>
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    <link:label id="lab_us-gaap_UseOfEstimates_019e83f7-3513-7919-b011-de2a6a89217b_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_019e83f7-3513-718c-9867-e19718201fe3_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 and Nonrelated Parties [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"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseDueFromAffiliates_019e83f7-3513-700d-a496-e19e43e74221_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseDueFromAffiliates" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Decrease (Increase) in Due from Affiliates</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseDueFromAffiliates_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseDueFromAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) Due from Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseDueFromAffiliates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseDueFromAffiliates"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable_019e83f7-3513-77c7-8f84-4f76bf634f47_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Income Tax Payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Income Taxes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable"/>
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    <link:label id="lab_us-gaap_PartnersCapitalAccountContributions_019e83f7-3513-7ebf-821a-619219e745d8_terseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountContributions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital Contributions on Purchases of Investments from Affiliates</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountContributions_019e83f7-3513-7981-8914-d33849508915_verboseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountContributions" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Capital contribution</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountContributions_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountContributions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partners' Capital Account, Contributions</link:label>
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    <link:label id="lab_us-gaap_GeneralPartnersCapitalAccount_label_en-US" xlink:label="lab_us-gaap_GeneralPartnersCapitalAccount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General Partners' Capital Account</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralPartnersCapitalAccount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralPartnersCapitalAccount"/>
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    <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_us-gaap_AssetsNet_019e83f7-3514-7f90-82d3-70eb3f16e5e2_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Assets</link:label>
    <link:label id="lab_us-gaap_AssetsNet_label_en-US" xlink:label="lab_us-gaap_AssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsNet" xlink:to="lab_us-gaap_AssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_019e83f7-3513-7d90-a27e-f4d2c69167a7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_019e83f7-3513-73dd-a6dd-b8843e8f30c3_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets, operating loss carryforwards</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019e83f7-3513-759f-9156-7e01c4ba440e_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_dei_EntityShellCompany_019e83f7-3513-750f-ba48-6f69d7927d66_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:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" 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_us-gaap_NoninterestExpenseDirectorsFees_019e83f7-3513-778a-be50-697e8e506c46_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestExpenseDirectorsFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Directors' Fees</link:label>
    <link:label id="lab_us-gaap_NoninterestExpenseDirectorsFees_label_en-US" xlink:label="lab_us-gaap_NoninterestExpenseDirectorsFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Director Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestExpenseDirectorsFees" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoninterestExpenseDirectorsFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestExpenseDirectorsFees" xlink:to="lab_us-gaap_NoninterestExpenseDirectorsFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_019e83f7-3513-7500-bb98-ca3dbffb00b3_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_us-gaap_IncomeTaxUncertaintiesPolicy_019e83f7-3513-7c40-8afb-55c9513dd7ca_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxUncertaintiesPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Uncertain Tax Positions</link:label>
    <link:label id="lab_us-gaap_IncomeTaxUncertaintiesPolicy_label_en-US" xlink:label="lab_us-gaap_IncomeTaxUncertaintiesPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Uncertainties, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxUncertaintiesPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxUncertaintiesPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxUncertaintiesPolicy" xlink:to="lab_us-gaap_IncomeTaxUncertaintiesPolicy" 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_bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember_019e83f7-3513-7064-8092-ebaa9c709df5_terseLabel_en-US" xlink:label="lab_bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Equity Investments And Primary Commitments</link:label>
    <link:label id="lab_bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember_label_en-US" xlink:label="lab_bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Equity Investments And Primary Commitments [Member]</link:label>
    <link:label id="lab_bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember_documentation_en-US" xlink:label="lab_bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Equity Investments And Primary Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember" xlink:href="bpef-20260630.xsd#bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember" xlink:to="lab_bpef_PrivateEquityInvestmentsAndPrimaryCommitmentsMember" 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>
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    <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_dei_DocumentFiscalPeriodFocus_019e83f7-3513-762d-ad3c-69f564b31b34_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>
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    <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_bpef_ExpensesAbsorbedByManagerMember_019e83f7-3513-769d-be1b-68e6869306b3_terseLabel_en-US" xlink:label="lab_bpef_ExpensesAbsorbedByManagerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenses Absorbed By Manager</link:label>
    <link:label id="lab_bpef_ExpensesAbsorbedByManagerMember_label_en-US" xlink:label="lab_bpef_ExpensesAbsorbedByManagerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Expenses Absorbed By Manager [Member]</link:label>
    <link:label id="lab_bpef_ExpensesAbsorbedByManagerMember_documentation_en-US" xlink:label="lab_bpef_ExpensesAbsorbedByManagerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Expenses Absorbed By Manager</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ExpensesAbsorbedByManagerMember" xlink:href="bpef-20260630.xsd#bpef_ExpensesAbsorbedByManagerMember"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
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    <link:label id="lab_us-gaap_InvestmentCompanyCapitalShareTransactionsAbstract_019e83f7-3513-77ce-8022-07f17b909f4c_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyCapitalShareTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital Unit Transactions</link:label>
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    <link:label id="lab_us-gaap_Liabilities_019e83f7-3513-7ade-a192-27c66b6974e1_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_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"/>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
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    <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"/>
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    <link:label id="lab_bpef_InvestmentsOwnedNumberOfInvestmentsAcquiredAtADiscount_documentation_en-US" xlink:label="lab_bpef_InvestmentsOwnedNumberOfInvestmentsAcquiredAtADiscount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments Owned, Number Of Investments Acquired At A Discount</link:label>
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    <link:label id="lab_bpef_DeferredTaxLiabilityOnPurchaseOfInvestmentFromAffiliate_019e83f7-3513-783f-8455-10f41d093339_terseLabel_en-US" xlink:label="lab_bpef_DeferredTaxLiabilityOnPurchaseOfInvestmentFromAffiliate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Tax Liability on Purchase of Investment from Affiliate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_bpef_DeferredTaxLiabilityOnPurchaseOfInvestmentFromAffiliate" xlink:href="bpef-20260630.xsd#bpef_DeferredTaxLiabilityOnPurchaseOfInvestmentFromAffiliate"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesMember_019e83f7-3513-7f34-b048-807a84dc2fe5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Debt</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities [Member]</link:label>
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    <link:label id="lab_us-gaap_CreditFacilityDomain_019e83f7-3513-7140-9230-671fad4df0ed_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: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>
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    <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_RelatedPartyTransactionLineItems_019e83f7-3513-794d-b5b2-35a8c45e948b_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_019e83f7-3513-70b4-9336-e6e3f3ec550c_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">Derivatives Instruments</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>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromLinesOfCredit_019e83f7-3513-72ac-ba25-1f3a27fb6126_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from Credit Facility Payable</link:label>
    <link:label id="lab_us-gaap_ProceedsFromLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_ProceedsFromLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromLinesOfCredit" xlink:to="lab_us-gaap_ProceedsFromLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019e83f7-3514-77c8-bd16-6d3f570b2226_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">Derivative Instruments</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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019e83f7-3513-74db-9f63-e3229065683f_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 Hierarchy Levels</link:label>
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    <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"/>
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    <link:label id="lab_us-gaap_DividendsReceivable_019fad25-b7f6-7845-92d8-98e71339042f_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend Receivable</link:label>
    <link:label id="lab_us-gaap_DividendsReceivable_label_en-US" xlink:label="lab_us-gaap_DividendsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsReceivable" xlink:to="lab_us-gaap_DividendsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherReceivables_019e83f7-3513-7690-b519-bbc9c0e886dc_terseLabel_en-US" xlink:label="lab_us-gaap_OtherReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from Affiliates</link:label>
    <link:label id="lab_us-gaap_OtherReceivables_019e83f7-3513-7902-825a-43a88d3ed727_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherReceivables" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Due from affiliates</link:label>
    <link:label id="lab_us-gaap_OtherReceivables_label_en-US" xlink:label="lab_us-gaap_OtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherReceivables" xlink:to="lab_us-gaap_OtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyFinancialHighlightsRollForward_019e83f7-3513-7ea1-afe0-15a82c05f92e_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_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>
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    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019e83f7-3513-7640-9339-2400849b2b3e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level I</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_019e83f7-3513-75ee-9ab9-b3b92df146da_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statutory rate</link:label>
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    <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"/>
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    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentIncomeLossRatio_019e83f7-3513-7ce7-a74a-d39433d18fad_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">Net Investment Income (Loss) (as percent)</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_bpef_ExpenseSupport_019e83f7-3513-7fc0-a863-cc3c0e9883da_terseLabel_en-US" xlink:label="lab_bpef_ExpenseSupport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expense Support</link:label>
    <link:label id="lab_bpef_ExpenseSupport_label_en-US" xlink:label="lab_bpef_ExpenseSupport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Expense Support</link:label>
    <link:label id="lab_bpef_ExpenseSupport_documentation_en-US" xlink:label="lab_bpef_ExpenseSupport" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Expense Support</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ExpenseSupport" xlink:href="bpef-20260630.xsd#bpef_ExpenseSupport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ExpenseSupport" xlink:to="lab_bpef_ExpenseSupport" 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_019e83f7-35de-7c2e-a3da-19de5a32c155_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_us-gaap_InvestmentCompanyExpenseAfterReductionOfFeeWaiverAndReimbursement_019e83f7-3513-72ae-a981-8e6f32f0b01c_totalLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyExpenseAfterReductionOfFeeWaiverAndReimbursement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Expenses</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyExpenseAfterReductionOfFeeWaiverAndReimbursement_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyExpenseAfterReductionOfFeeWaiverAndReimbursement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Expense, after Reduction of Fee Waiver and Reimbursement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyExpenseAfterReductionOfFeeWaiverAndReimbursement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyExpenseAfterReductionOfFeeWaiverAndReimbursement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyExpenseAfterReductionOfFeeWaiverAndReimbursement" xlink:to="lab_us-gaap_InvestmentCompanyExpenseAfterReductionOfFeeWaiverAndReimbursement" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_AdministrationFeeNetAssetValueThreshold_019e83f7-3513-72e3-8922-ad31934810c1_terseLabel_en-US" xlink:label="lab_bpef_AdministrationFeeNetAssetValueThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administration fee, net asset value thresholder</link:label>
    <link:label id="lab_bpef_AdministrationFeeNetAssetValueThreshold_label_en-US" xlink:label="lab_bpef_AdministrationFeeNetAssetValueThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administration Fee, Net Asset Value Threshold</link:label>
    <link:label id="lab_bpef_AdministrationFeeNetAssetValueThreshold_documentation_en-US" xlink:label="lab_bpef_AdministrationFeeNetAssetValueThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Administration Fee, Net Asset Value Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_AdministrationFeeNetAssetValueThreshold" xlink:href="bpef-20260630.xsd#bpef_AdministrationFeeNetAssetValueThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_AdministrationFeeNetAssetValueThreshold" xlink:to="lab_bpef_AdministrationFeeNetAssetValueThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019e83f7-3513-7983-a7b0-d97865522382_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <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"/>
    <link:label id="lab_srt_MinimumMember_019e83f7-3513-7ae0-af24-10ea8aae1454_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</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_LineOfCredit_019e83f7-3514-7904-9767-6e255d08fc96_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility Payable</link:label>
    <link:label id="lab_us-gaap_LineOfCredit_019e83f7-3514-7037-99e6-ea4dc74d7dd3_verboseLabel_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Outstanding under credit facility payable</link:label>
    <link:label id="lab_us-gaap_LineOfCredit_label_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCredit" xlink:to="lab_us-gaap_LineOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_019e83f7-3513-7b85-bd5e-f2b9a57696c9_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_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019e83f7-3513-7fc5-9a21-94f5b15257a4_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_bpef_PublicSecuritiesMember_019e83f7-3513-7d83-89b9-4118d2347020_terseLabel_en-US" xlink:label="lab_bpef_PublicSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Public Securities</link:label>
    <link:label id="lab_bpef_PublicSecuritiesMember_label_en-US" xlink:label="lab_bpef_PublicSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Public Securities [Member]</link:label>
    <link:label id="lab_bpef_PublicSecuritiesMember_documentation_en-US" xlink:label="lab_bpef_PublicSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Public Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PublicSecuritiesMember" xlink:href="bpef-20260630.xsd#bpef_PublicSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PublicSecuritiesMember" xlink:to="lab_bpef_PublicSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_019e83f7-3513-71f2-85b2-0baf82b36c3c_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"/>
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    <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_us-gaap_CashAndCashEquivalentsFairValueDisclosure_019e83f7-3514-7dac-b893-f55eb48ea38a_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:to="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_019e83f7-3514-78ac-8054-e88d88c0c3d7_terseLabel_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Limited partnership, units outstanding (in units)</link:label>
    <link:label id="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_019e83f7-3514-76a2-9e8e-294de038f75c_periodStartLabel_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Units Outstanding, beginning of the period (in units)</link:label>
    <link:label id="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_019e83f7-3514-70f9-9502-45b74b64de8c_periodEndLabel_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Units Outstanding, end of the period (in units)</link:label>
    <link:label id="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_label_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Limited Partners' Capital Account, Units Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding"/>
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    <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_019e83f7-3514-7dda-995e-22af43e0b724_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_019e83f7-3513-7dc4-9931-4c8da63e309d_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_srt_AffiliatedEntityMember_019e83f7-3514-7214-9e41-793d56f106a6_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_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_DerivativeTable_019e83f7-3513-796e-a928-5a6c05df9e47_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax_019e83f7-3513-7ee2-a219-393724ec1891_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 (Loss)</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeOperatingAfterExpenseAndTax_019e83f7-3513-7f15-9e10-a2c2ec5dbfd2_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 (Loss)</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_us-gaap_ScheduleOfProductInformationTable_019e83f7-3513-751b-8fd1-ac594004c893_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfProductInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nature of Operation, Product Information, Concentration of Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfProductInformationTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfProductInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nature of Operation, Product Information, Concentration of Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfProductInformationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfProductInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfProductInformationTable" xlink:to="lab_us-gaap_ScheduleOfProductInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_InvestmentCompanyManagementFeesWaivedRatio_019e83f7-3513-7e81-adc6-1c50bce0fa9d_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyManagementFeesWaivedRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Management Fees Waived (as percent)</link:label>
    <link:label id="lab_bpef_InvestmentCompanyManagementFeesWaivedRatio_label_en-US" xlink:label="lab_bpef_InvestmentCompanyManagementFeesWaivedRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Management Fees Waived Ratio</link:label>
    <link:label id="lab_bpef_InvestmentCompanyManagementFeesWaivedRatio_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyManagementFeesWaivedRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Management Fees Waived Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyManagementFeesWaivedRatio" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyManagementFeesWaivedRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyManagementFeesWaivedRatio" xlink:to="lab_bpef_InvestmentCompanyManagementFeesWaivedRatio" 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_us-gaap_RelatedPartyTransactionAxis_019e83f7-3513-78b3-b857-08a5087d6a56_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_bpef_InvestmentCompanyPerShareDataAbstract_019e83f7-3513-70f6-a6e4-4f4b6fc7253a_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyPerShareDataAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Per Unit Data</link:label>
    <link:label id="lab_bpef_InvestmentCompanyPerShareDataAbstract_label_en-US" xlink:label="lab_bpef_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_bpef_InvestmentCompanyPerShareDataAbstract_documentation_en-US" xlink:label="lab_bpef_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_bpef_InvestmentCompanyPerShareDataAbstract" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyPerShareDataAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyPerShareDataAbstract" xlink:to="lab_bpef_InvestmentCompanyPerShareDataAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_019e83f7-3513-70ec-898d-9a58f5673be7_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:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" 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"/>
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    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_019e83f7-3514-7a04-a354-9bff4b164329_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_bpef_ManagementAndServiceFeesBaseFeeTargetUnderWaiverAgreement_019e83f7-3513-7b45-b19e-f34690192e92_terseLabel_en-US" xlink:label="lab_bpef_ManagementAndServiceFeesBaseFeeTargetUnderWaiverAgreement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Target under waiver agreement (as percent)</link:label>
    <link:label id="lab_bpef_ManagementAndServiceFeesBaseFeeTargetUnderWaiverAgreement_label_en-US" xlink:label="lab_bpef_ManagementAndServiceFeesBaseFeeTargetUnderWaiverAgreement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management And Service Fees, Base Fee, Target Under Waiver Agreement</link:label>
    <link:label id="lab_bpef_ManagementAndServiceFeesBaseFeeTargetUnderWaiverAgreement_documentation_en-US" xlink:label="lab_bpef_ManagementAndServiceFeesBaseFeeTargetUnderWaiverAgreement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Management And Service Fees, Base Fee, Target Under Waiver Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ManagementAndServiceFeesBaseFeeTargetUnderWaiverAgreement" xlink:href="bpef-20260630.xsd#bpef_ManagementAndServiceFeesBaseFeeTargetUnderWaiverAgreement"/>
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    <link:label id="lab_bpef_NumberOfPromissoryNotes_label_en-US" xlink:label="lab_bpef_NumberOfPromissoryNotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Promissory Notes</link:label>
    <link:label id="lab_bpef_NumberOfPromissoryNotes_documentation_en-US" xlink:label="lab_bpef_NumberOfPromissoryNotes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Promissory Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_NumberOfPromissoryNotes" xlink:href="bpef-20260630.xsd#bpef_NumberOfPromissoryNotes"/>
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    <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>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
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    <link:label id="lab_srt_EuropeMember_019e83f7-3513-70ae-9734-a6ac0034874e_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"/>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_019e83f7-3513-71ed-972f-8f87627d4c90_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityAxis" xlink:to="lab_us-gaap_LineOfCreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyInvestmentOwnedFairValueMeasurementInput_019e83f7-3514-79af-9cd3-863a64d83932_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_019e83f7-3514-7a67-bb6e-f5bb6db269e7_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">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_ManagementFeeExpense_019e83f7-3513-7672-a8bd-6e9adee287a5_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</link:label>
    <link:label id="lab_us-gaap_ManagementFeeExpense_019e83f7-3513-7f62-bfce-bc30df2b7886_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_OpenForwardForeignCurrencyContractIdentifierAxis_019e83f7-3514-7306-979a-2e54a6c88aaa_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_bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue_019e83f7-3514-7644-b768-a187fa8346d1_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Early redemption fee penalty, proportion of net asset value (as percent)</link:label>
    <link:label id="lab_bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue_label_en-US" xlink:label="lab_bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Early Redemption Fee Penalty, Proportion Of Net Asset Value</link:label>
    <link:label id="lab_bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Early Redemption Fee Penalty, Proportion Of Net Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue" xlink:to="lab_bpef_InvestmentCompanyEarlyRedemptionFeePenaltyProportionOfNetAssetValue" 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_019e83f7-3513-7dac-a412-497f393117c5_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</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_019e83f7-3513-78c4-9edf-5fa452aed54a_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_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_MeasurementInputTypeDomain_019e83f7-3513-7cc4-aed9-52d70f07956e_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_019e83f7-3514-72a3-b91c-5b5e2d80d2ae_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 Change in Unrealized Gain (Loss) on Investments</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_us-gaap_PaymentsForPurchaseOfInvestmentOperatingActivity_019e83f7-3514-726e-81a4-3043b4524617_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_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_currency_EUR_019e83f7-3513-7ba5-aa54-27d6e17b1af5_terseLabel_en-US" xlink:label="lab_currency_EUR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EUR</link:label>
    <link:label id="lab_currency_EUR_label_en-US" xlink:label="lab_currency_EUR" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Euro Member Countries, Euro</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_currency_EUR" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_EUR"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_currency_EUR" xlink:to="lab_currency_EUR" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019e83f7-3513-7d5e-b931-161c4968395c_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_019e83f7-3513-7266-9b1a-3a5062caf053_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">Net assets at the beginning of the period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019e83f7-3513-7ebe-ae70-461422e2e15d_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">Net assets at the end of the period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <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_bpef_InvestmentCompanyExpenseSupportRatio_019e83f7-3514-7e4c-b1f0-64d9e042f587_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyExpenseSupportRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expense Support (as percent)</link:label>
    <link:label id="lab_bpef_InvestmentCompanyExpenseSupportRatio_label_en-US" xlink:label="lab_bpef_InvestmentCompanyExpenseSupportRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Expense Support Ratio</link:label>
    <link:label id="lab_bpef_InvestmentCompanyExpenseSupportRatio_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyExpenseSupportRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Expense Support Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyExpenseSupportRatio" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyExpenseSupportRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyExpenseSupportRatio" xlink:to="lab_bpef_InvestmentCompanyExpenseSupportRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressesAddressTypeAxis_019e83f7-3513-7370-b92f-6a1e62966d9b_terseLabel_en-US" xlink:label="lab_dei_EntityAddressesAddressTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Addresses, Address Type [Axis]</link:label>
    <link:label id="lab_dei_EntityAddressesAddressTypeAxis_label_en-US" xlink:label="lab_dei_EntityAddressesAddressTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Addresses, Address Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressesAddressTypeAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressesAddressTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressesAddressTypeAxis" xlink:to="lab_dei_EntityAddressesAddressTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncentiveFeePayable_019e83f7-3513-74e3-bf45-0329924aa631_terseLabel_en-US" xlink:label="lab_us-gaap_IncentiveFeePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation Payable</link:label>
    <link:label id="lab_us-gaap_IncentiveFeePayable_label_en-US" xlink:label="lab_us-gaap_IncentiveFeePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incentive Fee Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncentiveFeePayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncentiveFeePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncentiveFeePayable" xlink:to="lab_us-gaap_IncentiveFeePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019e83f7-3513-7b1d-bd88-7696f7f7b431_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_MeasurementInputEbitdaMultipleMember_019e83f7-3513-7201-ad98-edd2364d7aaf_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputEbitdaMultipleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBITDA Multiple</link:label>
    <link:label id="lab_us-gaap_MeasurementInputEbitdaMultipleMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputEbitdaMultipleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, EBITDA Multiple [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputEbitdaMultipleMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputEbitdaMultipleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputEbitdaMultipleMember" xlink:to="lab_us-gaap_MeasurementInputEbitdaMultipleMember" 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_us-gaap_ProfessionalFees_019e83f7-3513-7607-ab89-3bdf67d50f82_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_019e83f7-3513-71b2-9f93-c75f77592448_verboseLabel_en-US" xlink:label="lab_us-gaap_ProfessionalFees" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Professional fee</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_InterestIncomeOperating_019e83f7-3513-790e-8295-a44e2f1e0f71_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeOperating" 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_InterestIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeOperating" xlink:to="lab_us-gaap_InterestIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <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_bpef_CapitalUnitClassSMember_019e83f7-3514-7c3c-8391-ffd47fe78316_terseLabel_en-US" xlink:label="lab_bpef_CapitalUnitClassSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class S Units</link:label>
    <link:label id="lab_bpef_CapitalUnitClassSMember_label_en-US" xlink:label="lab_bpef_CapitalUnitClassSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Unit, Class S [Member]</link:label>
    <link:label id="lab_bpef_CapitalUnitClassSMember_documentation_en-US" xlink:label="lab_bpef_CapitalUnitClassSMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital Unit, Class S</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_CapitalUnitClassSMember" xlink:href="bpef-20260630.xsd#bpef_CapitalUnitClassSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_CapitalUnitClassSMember" xlink:to="lab_bpef_CapitalUnitClassSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019e83f7-3513-771d-a9d9-cc4698c28c2e_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_dei_EntityCentralIndexKey_019e83f7-3513-74f0-807c-ad427f28e991_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" 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_us-gaap_InvestmentCompanyChangesInNetAssetsTable_019e83f7-3513-7e97-8385-afd55ff85437_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyChangesInNetAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Company, Change in Net Assets [Table]</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyChangesInNetAssetsTable_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyChangesInNetAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Change in Net Assets [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyChangesInNetAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyChangesInNetAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyChangesInNetAssetsTable" xlink:to="lab_us-gaap_InvestmentCompanyChangesInNetAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_019e83f7-3513-7407-8cab-ef734195063e_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_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_bpef_PromissoryNotesPayableMember_019ffc77-98d2-7260-ac25-854d0d6ff59a_terseLabel_en-US" xlink:label="lab_bpef_PromissoryNotesPayableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Promissory Notes Payable</link:label>
    <link:label id="lab_bpef_PromissoryNotesPayableMember_label_en-US" xlink:label="lab_bpef_PromissoryNotesPayableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Promissory Notes Payable [Member]</link:label>
    <link:label id="lab_bpef_PromissoryNotesPayableMember_documentation_en-US" xlink:label="lab_bpef_PromissoryNotesPayableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Promissory Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PromissoryNotesPayableMember" xlink:href="bpef-20260630.xsd#bpef_PromissoryNotesPayableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PromissoryNotesPayableMember" xlink:to="lab_bpef_PromissoryNotesPayableMember" 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_019e83f7-3513-7422-89bf-56d5d2fb508c_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 and Deferred 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_019e83f7-3513-7c1d-b4e5-f710ddd6c0be_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 (Used in) Provided by 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <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_019e83f7-3514-7cc9-bd6d-e856613bc138_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_dei_DocumentTransitionReport_019e83f7-3513-7307-a8e8-061f80c549f7_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>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <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_bpef_PromissoryNotePayable_019e83f7-3513-7e65-86e8-5f916aa679da_terseLabel_en-US" xlink:label="lab_bpef_PromissoryNotePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Promissory Notes Payable</link:label>
    <link:label id="lab_bpef_PromissoryNotePayable_label_en-US" xlink:label="lab_bpef_PromissoryNotePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Promissory Note Payable</link:label>
    <link:label id="lab_bpef_PromissoryNotePayable_documentation_en-US" xlink:label="lab_bpef_PromissoryNotePayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Promissory Note Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PromissoryNotePayable" xlink:href="bpef-20260630.xsd#bpef_PromissoryNotePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PromissoryNotePayable" xlink:to="lab_bpef_PromissoryNotePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_AccruedServicingFees_019e83f7-3513-73c6-a7bf-636f8eb32da1_verboseLabel_en-US" xlink:label="lab_bpef_AccruedServicingFees" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued Servicing Fees</link:label>
    <link:label id="lab_bpef_AccruedServicingFees_019e83f7-3513-7dc1-a580-884cb01c02ce_terseLabel_en-US" xlink:label="lab_bpef_AccruedServicingFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued servicing fees</link:label>
    <link:label id="lab_bpef_AccruedServicingFees_label_en-US" xlink:label="lab_bpef_AccruedServicingFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Servicing Fees</link:label>
    <link:label id="lab_bpef_AccruedServicingFees_documentation_en-US" xlink:label="lab_bpef_AccruedServicingFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Servicing Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_AccruedServicingFees" xlink:href="bpef-20260630.xsd#bpef_AccruedServicingFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_AccruedServicingFees" xlink:to="lab_bpef_AccruedServicingFees" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_NotesPayableInterestPaidInKind_019faf53-6510-7c3c-ae70-aef2bc5081c2_terseLabel_en-US" xlink:label="lab_bpef_NotesPayableInterestPaidInKind" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid in kind</link:label>
    <link:label id="lab_bpef_NotesPayableInterestPaidInKind_label_en-US" xlink:label="lab_bpef_NotesPayableInterestPaidInKind" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Interest Paid In Kind</link:label>
    <link:label id="lab_bpef_NotesPayableInterestPaidInKind_documentation_en-US" xlink:label="lab_bpef_NotesPayableInterestPaidInKind" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Payable, Interest Paid In Kind</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_NotesPayableInterestPaidInKind" xlink:href="bpef-20260630.xsd#bpef_NotesPayableInterestPaidInKind"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_NotesPayableInterestPaidInKind" xlink:to="lab_bpef_NotesPayableInterestPaidInKind" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019e83f7-3513-7eca-a891-2a577d2427a4_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_019e83f7-3513-7d01-b388-67153ccd65f8_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_InvestmentCompanyIssuanceOfSharesPerShare_019e83f7-35de-7e5a-b2c8-388a2965be42_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyIssuanceOfSharesPerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Share issuance (in USD per unit)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyIssuanceOfSharesPerShare_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyIssuanceOfSharesPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Share Issuance, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyIssuanceOfSharesPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyIssuanceOfSharesPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyIssuanceOfSharesPerShare" xlink:to="lab_us-gaap_InvestmentCompanyIssuanceOfSharesPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_019e83f7-35de-70c7-9724-44f6fc290285_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenses</link:label>
    <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_bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember_019e83f7-3513-70d9-bfaf-fc9bae1a60eb_terseLabel_en-US" xlink:label="lab_bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Brookfield Private Equity Group Manager Holdings LP</link:label>
    <link:label id="lab_bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember_label_en-US" xlink:label="lab_bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Brookfield Private Equity Group Manager Holdings LP [Member]</link:label>
    <link:label id="lab_bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember_documentation_en-US" xlink:label="lab_bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Brookfield Private Equity Group Manager Holdings LP</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember" xlink:href="bpef-20260630.xsd#bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember" xlink:to="lab_bpef_BrookfieldPrivateEquityGroupManagerHoldingsLPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019e83f7-35de-7bc4-80fa-d69c2f73150e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable rate (as percent)</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses_019e83f7-3513-75fa-b9e6-e82e11ea547b_terseLabel_en-US" xlink:label="lab_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expense support, period to forgo management fee to offset expenses</link:label>
    <link:label id="lab_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses_019e83f7-3513-7030-b430-7bb421cc78e0_verboseLabel_en-US" xlink:label="lab_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Expense support, period to forgo management fee to offset expenses (in months)</link:label>
    <link:label id="lab_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses_label_en-US" xlink:label="lab_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Expense Support, Period To Forgo Management Fee To Offset Expenses</link:label>
    <link:label id="lab_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses_documentation_en-US" xlink:label="lab_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Expense Support, Period To Forgo Management Fee To Offset Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses" xlink:href="bpef-20260630.xsd#bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses" xlink:to="lab_bpef_ExpenseSupportPeriodToForgoManagementFeeToOffsetExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019e83f7-35de-7e47-8aae-e15d3d3384af_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:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" 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_dei_DocumentInformationTable_019e83f7-3514-75e6-b27c-adecd0f3044b_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" 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_SubsequentEventsTextBlock_019e83f7-3513-79ed-9038-e0bbf603761b_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_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_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019e83f7-3513-7ac4-968c-b6655620316b_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_ManagementAndIncentiveFeesExpense_019fd3f5-2df3-78fb-912a-8a734856398a_terseLabel_en-US" xlink:label="lab_us-gaap_ManagementAndIncentiveFeesExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued performance participation allocation</link:label>
    <link:label id="lab_us-gaap_ManagementAndIncentiveFeesExpense_label_en-US" xlink:label="lab_us-gaap_ManagementAndIncentiveFeesExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management and Incentive Fees Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementAndIncentiveFeesExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ManagementAndIncentiveFeesExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ManagementAndIncentiveFeesExpense" xlink:to="lab_us-gaap_ManagementAndIncentiveFeesExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_ServicingFeesIncurredButNotYetPaid_019e83f7-3513-79fc-8e7a-1c52486a1c28_terseLabel_en-US" xlink:label="lab_bpef_ServicingFeesIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued Servicing Fees</link:label>
    <link:label id="lab_bpef_ServicingFeesIncurredButNotYetPaid_label_en-US" xlink:label="lab_bpef_ServicingFeesIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Fees Incurred But Not Yet Paid</link:label>
    <link:label id="lab_bpef_ServicingFeesIncurredButNotYetPaid_documentation_en-US" xlink:label="lab_bpef_ServicingFeesIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Servicing Fees Incurred But Not Yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ServicingFeesIncurredButNotYetPaid" xlink:href="bpef-20260630.xsd#bpef_ServicingFeesIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ServicingFeesIncurredButNotYetPaid" xlink:to="lab_bpef_ServicingFeesIncurredButNotYetPaid" 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_us-gaap_StatementLineItems_019e83f7-3513-769b-9e25-a7424b39c0dd_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_019e83f7-3513-76c2-b9ab-6fd9a1291432_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_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_bpef_ExpenseSupportFeeReimbursement_019e83f7-3514-7659-85e4-015a54948687_terseLabel_en-US" xlink:label="lab_bpef_ExpenseSupportFeeReimbursement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expense support reimbursement</link:label>
    <link:label id="lab_bpef_ExpenseSupportFeeReimbursement_label_en-US" xlink:label="lab_bpef_ExpenseSupportFeeReimbursement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Expense Support, Fee Reimbursement</link:label>
    <link:label id="lab_bpef_ExpenseSupportFeeReimbursement_documentation_en-US" xlink:label="lab_bpef_ExpenseSupportFeeReimbursement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Expense Support, Fee Reimbursement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ExpenseSupportFeeReimbursement" xlink:href="bpef-20260630.xsd#bpef_ExpenseSupportFeeReimbursement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ExpenseSupportFeeReimbursement" xlink:to="lab_bpef_ExpenseSupportFeeReimbursement" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest_019fae69-688d-7e77-8d4d-4ce7544457af_terseLabel_en-US" xlink:label="lab_bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of investments with increased interest</link:label>
    <link:label id="lab_bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest_label_en-US" xlink:label="lab_bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments Owned, Number Of Investments With Increased Interest</link:label>
    <link:label id="lab_bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest_documentation_en-US" xlink:label="lab_bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments Owned, Number Of Investments With Increased Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest" xlink:href="bpef-20260630.xsd#bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest" xlink:to="lab_bpef_InvestmentsOwnedNumberOfInvestmentsWithIncreasedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesByIndustryAxis_019e83f7-3513-75b1-8db8-2fcf972560b2_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_bpef_CapitalUnitClassIMember_019e83f7-3513-7cbb-997e-ede24d990f5d_terseLabel_en-US" xlink:label="lab_bpef_CapitalUnitClassIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class I Units</link:label>
    <link:label id="lab_bpef_CapitalUnitClassIMember_label_en-US" xlink:label="lab_bpef_CapitalUnitClassIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Unit, Class I [Member]</link:label>
    <link:label id="lab_bpef_CapitalUnitClassIMember_documentation_en-US" xlink:label="lab_bpef_CapitalUnitClassIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital Unit, Class I</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_CapitalUnitClassIMember" xlink:href="bpef-20260630.xsd#bpef_CapitalUnitClassIMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_CapitalUnitClassIMember" xlink:to="lab_bpef_CapitalUnitClassIMember" 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"/>
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    <link:label id="lab_us-gaap_ManagementAndServiceFeesRate_019e83f7-3513-7b01-a947-8eb68d8b2c9b_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">Fee rate (as percent)</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"/>
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    <link:label id="lab_bpef_InvestmentCompanyServicingFeePerShare_019e83f7-3514-7ecb-83e1-0eb4969f83ce_netLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyServicingFeePerShare" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Servicing Fees (in USD per unit)</link:label>
    <link:label id="lab_bpef_InvestmentCompanyServicingFeePerShare_label_en-US" xlink:label="lab_bpef_InvestmentCompanyServicingFeePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Servicing Fee, Per Share</link:label>
    <link:label id="lab_bpef_InvestmentCompanyServicingFeePerShare_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyServicingFeePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Servicing Fee, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyServicingFeePerShare" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyServicingFeePerShare"/>
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    <link:label id="lab_bpef_InvestmentCompanyDeferredTaxLiabilitiesOnContributedInvestmentPerShare_019e83f7-3514-72d3-8b9c-7da60f1ec127_negatedTerseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyDeferredTaxLiabilitiesOnContributedInvestmentPerShare" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Allocation of Deferred Tax Liability on Purchase of Investment from Affiliate (in USD per unit)</link:label>
    <link:label id="lab_bpef_InvestmentCompanyDeferredTaxLiabilitiesOnContributedInvestmentPerShare_label_en-US" xlink:label="lab_bpef_InvestmentCompanyDeferredTaxLiabilitiesOnContributedInvestmentPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Deferred Tax Liabilities On Contributed Investment, Per Share</link:label>
    <link:label id="lab_bpef_InvestmentCompanyDeferredTaxLiabilitiesOnContributedInvestmentPerShare_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyDeferredTaxLiabilitiesOnContributedInvestmentPerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Deferred Tax Liabilities On Contributed Investment, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyDeferredTaxLiabilitiesOnContributedInvestmentPerShare" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyDeferredTaxLiabilitiesOnContributedInvestmentPerShare"/>
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    <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"/>
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    <link:label id="lab_us-gaap_ProductInformationLineItems_019e83f7-3513-7822-8096-abddeaeac6dd_terseLabel_en-US" xlink:label="lab_us-gaap_ProductInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_ProductInformationLineItems_label_en-US" xlink:label="lab_us-gaap_ProductInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProductInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductInformationLineItems" xlink:to="lab_us-gaap_ProductInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_019e83f7-3513-7bd4-af16-f0fda99fddd1_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"/>
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    <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_RevolvingCreditFacilityMember_019e83f7-3514-74a9-9a4b-b90b3323994f_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_InvestmentCompanyChangesInNetAssetsLineItems_019e83f7-3513-7056-b7a1-a60335b04af8_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyChangesInNetAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Company, Change in Net Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyChangesInNetAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyChangesInNetAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Change in Net Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyChangesInNetAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyChangesInNetAssetsLineItems"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_019e83f7-3513-7a2b-8783-394fc5ea7b39_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 of Investments and Financial Instruments, Investments at Fair Value</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_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyAbstract" xlink:to="lab_us-gaap_InvestmentCompanyAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <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_us-gaap_InvestmentCompanyInvestmentIncomeLossFromOperationsPerShare_019e83f7-35de-77a2-9ab7-451b08464a90_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 in Net Assets Resulting from Investment Operations (in USD per unit)</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"/>
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    <link:label id="lab_bpef_NetUnrealizedGainsLossesAbstract_019e83f7-3513-7bb6-88f5-d57bd704600a_terseLabel_en-US" xlink:label="lab_bpef_NetUnrealizedGainsLossesAbstract" 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_bpef_NetUnrealizedGainsLossesAbstract_label_en-US" xlink:label="lab_bpef_NetUnrealizedGainsLossesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Unrealized Gains (Losses) [Abstract]</link:label>
    <link:label id="lab_bpef_NetUnrealizedGainsLossesAbstract_documentation_en-US" xlink:label="lab_bpef_NetUnrealizedGainsLossesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Unrealized Gains (Losses)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_NetUnrealizedGainsLossesAbstract" xlink:href="bpef-20260630.xsd#bpef_NetUnrealizedGainsLossesAbstract"/>
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    <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"/>
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    <link:label id="lab_dei_EntityCurrentReportingStatus_019e83f7-3513-79bb-93fa-ad554fba3229_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:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" 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"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e83f7-3513-71ef-8a8d-a3c8ec0e1fcf_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 (Used in) Provided by 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"/>
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    <link:label id="lab_bpef_ServicingFeesPolicyTextBlock_019e83f7-3514-79bc-876a-33a540e5b372_terseLabel_en-US" xlink:label="lab_bpef_ServicingFeesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Fees</link:label>
    <link:label id="lab_bpef_ServicingFeesPolicyTextBlock_label_en-US" xlink:label="lab_bpef_ServicingFeesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Fees [Policy Text Block]</link:label>
    <link:label id="lab_bpef_ServicingFeesPolicyTextBlock_documentation_en-US" xlink:label="lab_bpef_ServicingFeesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Servicing Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ServicingFeesPolicyTextBlock" xlink:href="bpef-20260630.xsd#bpef_ServicingFeesPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_019e83f7-3514-7f60-a341-58443ad26ce1_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Change in Unrealized Gain (Loss) on Investments</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_019e83f7-3514-7dda-be79-f9e6dc7d45e8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net Change in Unrealized Gain (Loss) on Investments</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Investments</link:label>
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    <link:label id="lab_us-gaap_IncentiveFeeExpense_019e83f7-3513-7602-8f41-0956ed4014d4_terseLabel_en-US" xlink:label="lab_us-gaap_IncentiveFeeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation</link:label>
    <link:label id="lab_us-gaap_IncentiveFeeExpense_label_en-US" xlink:label="lab_us-gaap_IncentiveFeeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incentive Fee Expense</link:label>
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    <link:label id="lab_bpef_InvestmentCompanyTotalReturnTransactional_019e83f7-3514-71d1-9343-cb1473136d14_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyTotalReturnTransactional" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total return calculated on Transactional NAV</link:label>
    <link:label id="lab_bpef_InvestmentCompanyTotalReturnTransactional_label_en-US" xlink:label="lab_bpef_InvestmentCompanyTotalReturnTransactional" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Total Return, Transactional</link:label>
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    <link:label id="lab_us-gaap_InvestmentCompanyIncentiveAllocationToAverageNetAssets_019e83f7-3513-7460-92c9-5db44376335e_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyIncentiveAllocationToAverageNetAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation (as percent)</link:label>
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    <link:label id="lab_bpef_RedemptionPayableToAffiliates_documentation_en-US" xlink:label="lab_bpef_RedemptionPayableToAffiliates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redemption Payable To Affiliates</link:label>
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    <link:label id="lab_us-gaap_InvestmentCompanyTotalReturn_019e83f7-3513-7c27-b64f-7f015c241b65_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 Net Asset Value (as percent)</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>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Note [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteAbstract" xlink:to="lab_us-gaap_StockholdersEquityNoteAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationalCostExpense_019e83f7-3513-716e-9229-3a9821037546_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationalCostExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organizational Expenses</link:label>
    <link:label id="lab_us-gaap_OrganizationalCostExpense_019e83f7-3513-7510-a4c2-505a3e511c27_verboseLabel_en-US" xlink:label="lab_us-gaap_OrganizationalCostExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Organizational expenses</link:label>
    <link:label id="lab_us-gaap_OrganizationalCostExpense_label_en-US" xlink:label="lab_us-gaap_OrganizationalCostExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organizational Cost, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationalCostExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationalCostExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationalCostExpense" xlink:to="lab_us-gaap_OrganizationalCostExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilities_019e83f7-3514-7efd-82f0-6150a5d4557c_terseLabel_en-US" xlink:label="lab_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities in Excess of Other Assets</link:label>
    <link:label id="lab_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilities_label_en-US" xlink:label="lab_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninvestment Assets Less Noninvestment Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilities" xlink:to="lab_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019e83f7-3513-7062-99f9-828b2b109186_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">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_currency_GBP_019e83f7-3513-79e0-affd-5431e85bd0e9_terseLabel_en-US" xlink:label="lab_currency_GBP" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GBP</link:label>
    <link:label id="lab_currency_GBP_label_en-US" xlink:label="lab_currency_GBP" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">United Kingdom, Pounds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_currency_GBP" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_GBP"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_currency_GBP" xlink:to="lab_currency_GBP" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019e83f7-3514-776e-91d4-6386e2312f8b_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_bpef_RelatedPartyTransactionTerm_019e83f7-3513-7375-ac5f-9bae0094797f_terseLabel_en-US" xlink:label="lab_bpef_RelatedPartyTransactionTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, term (in months)</link:label>
    <link:label id="lab_bpef_RelatedPartyTransactionTerm_label_en-US" xlink:label="lab_bpef_RelatedPartyTransactionTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Term</link:label>
    <link:label id="lab_bpef_RelatedPartyTransactionTerm_documentation_en-US" xlink:label="lab_bpef_RelatedPartyTransactionTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_RelatedPartyTransactionTerm" xlink:href="bpef-20260630.xsd#bpef_RelatedPartyTransactionTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_RelatedPartyTransactionTerm" xlink:to="lab_bpef_RelatedPartyTransactionTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_CapitalUnitClassDMember_019e83f7-3513-734d-943c-a35715e3d17f_terseLabel_en-US" xlink:label="lab_bpef_CapitalUnitClassDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class D Units</link:label>
    <link:label id="lab_bpef_CapitalUnitClassDMember_label_en-US" xlink:label="lab_bpef_CapitalUnitClassDMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Unit, Class D [Member]</link:label>
    <link:label id="lab_bpef_CapitalUnitClassDMember_documentation_en-US" xlink:label="lab_bpef_CapitalUnitClassDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital Unit, Class D</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_CapitalUnitClassDMember" xlink:href="bpef-20260630.xsd#bpef_CapitalUnitClassDMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_CapitalUnitClassDMember" xlink:to="lab_bpef_CapitalUnitClassDMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncome_019e83f7-3513-7689-a053-fdd51ea97b85_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncome" 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_OtherIncome_label_en-US" xlink:label="lab_us-gaap_OtherIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncome" xlink:to="lab_us-gaap_OtherIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_019e83f7-3514-70b4-ae8a-67779d084874_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Assets at Fair Value</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_019e83f7-3514-78f4-8716-3dd8cc2dd9a5_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 Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_019e83f7-3514-77ae-9e58-9936a1b0534d_netLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Fair Value</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_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <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_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectDisposalGroupIncludingDiscontinuedOperations_019e83f7-35de-7ed7-b591-09bdce519189_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectDisposalGroupIncludingDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Increase (Decrease) in Cash During the Period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectDisposalGroupIncludingDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectDisposalGroupIncludingDiscontinuedOperations" 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, Period Increase (Decrease), Including Exchange Rate Effect, Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectDisposalGroupIncludingDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectDisposalGroupIncludingDiscontinuedOperations"/>
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    <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_us-gaap_InvestmentCompanyFinancialHighlightsTableTextBlock_019e83f7-3514-7475-9261-2ea07b2240b7_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"/>
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    <link:label id="lab_us-gaap_Cash_019e83f7-35de-7d65-bc2e-6a6d4937b566_terseLabel_en-US" xlink:label="lab_us-gaap_Cash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_Cash_label_en-US" xlink:label="lab_us-gaap_Cash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Cash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Cash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Cash" xlink:to="lab_us-gaap_Cash" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AddressTypeDomain_019e83f7-35de-78bc-884d-2e5965792057_terseLabel_en-US" xlink:label="lab_dei_AddressTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Address Type [Domain]</link:label>
    <link:label id="lab_dei_AddressTypeDomain_label_en-US" xlink:label="lab_dei_AddressTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Address Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AddressTypeDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AddressTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AddressTypeDomain" xlink:to="lab_dei_AddressTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_ExpenseSupportPolicyTextBlock_019e83f7-3514-766c-946f-41f191d22031_terseLabel_en-US" xlink:label="lab_bpef_ExpenseSupportPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expense Support</link:label>
    <link:label id="lab_bpef_ExpenseSupportPolicyTextBlock_label_en-US" xlink:label="lab_bpef_ExpenseSupportPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Expense Support [Policy Text Block]</link:label>
    <link:label id="lab_bpef_ExpenseSupportPolicyTextBlock_documentation_en-US" xlink:label="lab_bpef_ExpenseSupportPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Expense Support</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ExpenseSupportPolicyTextBlock" xlink:href="bpef-20260630.xsd#bpef_ExpenseSupportPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019e83f7-3514-7ccc-94bb-83c291cd8a63_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">Related Party Transaction [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"/>
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    <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"/>
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    <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_bpef_RedemptionsAndDiscountPayableToAffiliates_019e83f7-3513-793a-975f-e0d5eead127b_terseLabel_en-US" xlink:label="lab_bpef_RedemptionsAndDiscountPayableToAffiliates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class B-1 Redemptions Payable to Affiliates and Class B-1 Redemption Discount Payable</link:label>
    <link:label id="lab_bpef_RedemptionsAndDiscountPayableToAffiliates_label_en-US" xlink:label="lab_bpef_RedemptionsAndDiscountPayableToAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redemptions And Discount Payable To Affiliates</link:label>
    <link:label id="lab_bpef_RedemptionsAndDiscountPayableToAffiliates_documentation_en-US" xlink:label="lab_bpef_RedemptionsAndDiscountPayableToAffiliates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redemptions And Discount Payable To Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_RedemptionsAndDiscountPayableToAffiliates" xlink:href="bpef-20260630.xsd#bpef_RedemptionsAndDiscountPayableToAffiliates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_RedemptionsAndDiscountPayableToAffiliates" xlink:to="lab_bpef_RedemptionsAndDiscountPayableToAffiliates" 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_bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare_019e83f7-3514-7fcd-b9a3-8359d071b061_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allocation of Discount on Redemption (in USD per unit)</link:label>
    <link:label id="lab_bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare_label_en-US" xlink:label="lab_bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Allocation Of Discount On Redemption, Per Share</link:label>
    <link:label id="lab_bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Allocation Of Discount On Redemption, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare" xlink:to="lab_bpef_InvestmentCompanyAllocationOfDiscountOnRedemptionPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019e83f7-3513-706e-a92e-9b29f610cb87_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:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" 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_us-gaap_LimitedPartnersCapitalAccountUnitsIssued_019e83f7-3513-759f-ae96-76d50301b619_terseLabel_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Limited partnership, units issued (in units)</link:label>
    <link:label id="lab_us-gaap_LimitedPartnersCapitalAccountUnitsIssued_label_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Limited Partners' Capital Account, Units Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedPartnersCapitalAccountUnitsIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:to="lab_us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedBalanceShares_019e83f7-3513-73b0-9d23-9d13b8e7701f_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">Principal amount, shares (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_019e83f7-3513-7506-b123-9779902fc721_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_us-gaap_RelatedPartyTransactionDomain_019e83f7-3513-78c9-9288-1f69412476f1_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_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability_019e83f7-3513-752b-adca-ef485a6eb494_negatedTerseLabel_en-US" xlink:label="lab_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deferred Tax Liability on Purchase of Investment from Affiliate</link:label>
    <link:label id="lab_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability_019e83f7-3513-77d1-b9fa-447a2165b65c_terseLabel_en-US" xlink:label="lab_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities in connection with acquisition</link:label>
    <link:label id="lab_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability_label_en-US" xlink:label="lab_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Deferred Tax Liability</link:label>
    <link:label id="lab_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability_documentation_en-US" xlink:label="lab_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Deferred Tax Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability" xlink:href="bpef-20260630.xsd#bpef_StockIssuedDuringPeriodValueDeferredTaxLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability" xlink:to="lab_bpef_StockIssuedDuringPeriodValueDeferredTaxLiability" 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_bpef_ValuationTechniqueHypotheticalLiquidationApproachMember_019e83f7-3514-720c-95f3-1c9dbc705b26_terseLabel_en-US" xlink:label="lab_bpef_ValuationTechniqueHypotheticalLiquidationApproachMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hypothetical Liquidation Approach</link:label>
    <link:label id="lab_bpef_ValuationTechniqueHypotheticalLiquidationApproachMember_label_en-US" xlink:label="lab_bpef_ValuationTechniqueHypotheticalLiquidationApproachMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Hypothetical Liquidation Approach [Member]</link:label>
    <link:label id="lab_bpef_ValuationTechniqueHypotheticalLiquidationApproachMember_documentation_en-US" xlink:label="lab_bpef_ValuationTechniqueHypotheticalLiquidationApproachMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Hypothetical Liquidation Approach</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ValuationTechniqueHypotheticalLiquidationApproachMember" xlink:href="bpef-20260630.xsd#bpef_ValuationTechniqueHypotheticalLiquidationApproachMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ValuationTechniqueHypotheticalLiquidationApproachMember" xlink:to="lab_bpef_ValuationTechniqueHypotheticalLiquidationApproachMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019e83f7-3514-7fc6-88a0-1196f067d93f_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" 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_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_019e83f7-3513-72d3-adbc-f84cfc01299e_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">Investments at Fair Value</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedAtFairValue_019e83f7-3513-748c-a013-172f4676710a_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">Fair Value</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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentOwnedAtFairValue" xlink:to="lab_us-gaap_InvestmentOwnedAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesMember_019e83f7-3513-74fa-8f00-cbec885ce1fe_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">Portfolio Companies</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_bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember_019e83f7-3513-74a7-8425-659b081167e4_terseLabel_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Annual Hurdle Rate</link:label>
    <link:label id="lab_bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember_label_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation - Incentive Rate, Annual Hurdle Rate [Member]</link:label>
    <link:label id="lab_bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember_documentation_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation - Incentive Rate, Annual Hurdle Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember" xlink:href="bpef-20260630.xsd#bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember" xlink:to="lab_bpef_PerformanceParticipationAllocationIncentiveRateAnnualHurdleRateMember" 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_us-gaap_AdministrativeFeesExpense_019e83f7-3513-7ed7-90c6-dc2023432696_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">Administration Fees</link:label>
    <link:label id="lab_us-gaap_AdministrativeFeesExpense_019e83f7-3513-77af-abb1-4ec2ba46257c_verboseLabel_en-US" xlink:label="lab_us-gaap_AdministrativeFeesExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Administrative fees</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_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_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019e83f7-3514-77f5-b47a-96ca8eaf9e1b_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" 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_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019e83f7-3514-7fba-8ab9-9da8c68f0f3b_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">Ending balance</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_bpef_InvestmentCompanyTaxBasisInvestmentAcquired_019fd41a-be23-79ad-9b72-75d940c124d7_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyTaxBasisInvestmentAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Taxes incurred from investment acquired</link:label>
    <link:label id="lab_bpef_InvestmentCompanyTaxBasisInvestmentAcquired_label_en-US" xlink:label="lab_bpef_InvestmentCompanyTaxBasisInvestmentAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Tax Basis, Investment Acquired</link:label>
    <link:label id="lab_bpef_InvestmentCompanyTaxBasisInvestmentAcquired_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyTaxBasisInvestmentAcquired" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Tax Basis, Investment Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyTaxBasisInvestmentAcquired" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyTaxBasisInvestmentAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyTaxBasisInvestmentAcquired" xlink:to="lab_bpef_InvestmentCompanyTaxBasisInvestmentAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToReportingEntityAbstract_019e83f7-3513-7cc0-bb74-4d76f653eff6_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operations</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToReportingEntityAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToReportingEntityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:to="lab_us-gaap_NetIncomeLossAttributableToReportingEntityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock_019e83f7-3513-7074-8bfb-22327f0653e0_terseLabel_en-US" xlink:label="lab_bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organizational, Offering and Other Fund Expenses</link:label>
    <link:label id="lab_bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock_label_en-US" xlink:label="lab_bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organizational, Offering And Fund Expenses, Policy [Policy Text Block]</link:label>
    <link:label id="lab_bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Organizational, Offering And Fund Expenses, Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock" xlink:href="bpef-20260630.xsd#bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock" xlink:to="lab_bpef_OrganizationalOfferingAndFundExpensesPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_ServicingFeesExpense_019fd3fc-e292-7172-ae1c-24e170e4f7cf_terseLabel_en-US" xlink:label="lab_bpef_ServicingFeesExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing fees charged</link:label>
    <link:label id="lab_bpef_ServicingFeesExpense_label_en-US" xlink:label="lab_bpef_ServicingFeesExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Fees Expense</link:label>
    <link:label id="lab_bpef_ServicingFeesExpense_documentation_en-US" xlink:label="lab_bpef_ServicingFeesExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Servicing Fees Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ServicingFeesExpense" xlink:href="bpef-20260630.xsd#bpef_ServicingFeesExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ServicingFeesExpense" xlink:to="lab_bpef_ServicingFeesExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019e83f7-3513-7013-9db4-14f2e1df2c86_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_srt_CurrencyAxis_019e83f7-3513-78d8-b40c-4d1e93f74869_terseLabel_en-US" xlink:label="lab_srt_CurrencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Currency [Axis]</link:label>
    <link:label id="lab_srt_CurrencyAxis_label_en-US" xlink:label="lab_srt_CurrencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Currency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CurrencyAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CurrencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CurrencyAxis" xlink:to="lab_srt_CurrencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonLimitedPartnersUnits_019e83f7-3513-71f6-b282-225334ccc772_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonLimitedPartnersUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Units</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonLimitedPartnersUnits_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonLimitedPartnersUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Limited Partners Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonLimitedPartnersUnits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfCommonLimitedPartnersUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonLimitedPartnersUnits" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonLimitedPartnersUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019e83f7-3513-7078-a516-04667007a642_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:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" 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_bpef_InvestmentOwnedNumberOfInvestmentsExchanged_019e83f7-3514-7a68-92c9-e8faab538571_terseLabel_en-US" xlink:label="lab_bpef_InvestmentOwnedNumberOfInvestmentsExchanged" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of investments exchanged</link:label>
    <link:label id="lab_bpef_InvestmentOwnedNumberOfInvestmentsExchanged_label_en-US" xlink:label="lab_bpef_InvestmentOwnedNumberOfInvestmentsExchanged" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Number Of Investments Exchanged</link:label>
    <link:label id="lab_bpef_InvestmentOwnedNumberOfInvestmentsExchanged_documentation_en-US" xlink:label="lab_bpef_InvestmentOwnedNumberOfInvestmentsExchanged" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Owned, Number Of Investments Exchanged</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentOwnedNumberOfInvestmentsExchanged" xlink:href="bpef-20260630.xsd#bpef_InvestmentOwnedNumberOfInvestmentsExchanged"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentOwnedNumberOfInvestmentsExchanged" xlink:to="lab_bpef_InvestmentOwnedNumberOfInvestmentsExchanged" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_019e83f7-35de-7b0a-99f1-b0ad81faf58a_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Net</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_019e83f7-35de-73b6-b0c8-8d76c5a10ddf_verboseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities, net</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" 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_dei_EntitySmallBusiness_019e83f7-3514-7d3b-b619-522c5478c655_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:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" 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_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_bpef_BusinessServicesSectorMember_019e83f7-3514-7fc9-a52d-cb95e2203d75_terseLabel_en-US" xlink:label="lab_bpef_BusinessServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Services</link:label>
    <link:label id="lab_bpef_BusinessServicesSectorMember_label_en-US" xlink:label="lab_bpef_BusinessServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Services Sector [Member]</link:label>
    <link:label id="lab_bpef_BusinessServicesSectorMember_documentation_en-US" xlink:label="lab_bpef_BusinessServicesSectorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Services Sector</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_BusinessServicesSectorMember" xlink:href="bpef-20260630.xsd#bpef_BusinessServicesSectorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_BusinessServicesSectorMember" xlink:to="lab_bpef_BusinessServicesSectorMember" 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_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_019e83f7-3513-7c32-9faa-762836e8370b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" 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_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_LineOfCreditFacilityLenderDomain_019e83f7-3514-7ed1-abb8-3ffb6c77c320_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLenderDomain_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityLenderDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:to="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019e83f7-3513-7689-8f80-2422d8e14ae9_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:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" 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_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_019e83f7-3514-73e8-b667-a2316007bc20_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" 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_us-gaap_NetAssetValuePerShare_019e83f7-3513-75fb-bfc2-b7723aaeddf4_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 per Unit, beginning balance (in USD per unit)</link:label>
    <link:label id="lab_us-gaap_NetAssetValuePerShare_019e83f7-3513-7ebb-86a1-b2c4ec3cafad_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 per Unit, ending balance (in USD per unit)</link:label>
    <link:label id="lab_us-gaap_NetAssetValuePerShare_label_en-US" xlink:label="lab_us-gaap_NetAssetValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Asset Value 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_019e83f7-3514-7c3b-bb60-172c6f248aba_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">Summary of 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_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract_019e83f7-3514-76d5-9dc2-ba6ba29f957b_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract" 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, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract" 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_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_019e83f7-3513-718e-a670-07efb0285097_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:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" 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_dei_EntityAddressPostalZipCode_019e83f7-3513-71e2-a2cc-2fe9e199a74e_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:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" 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_019e83f7-3513-7b6f-97a1-72a9a9a9faf6_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:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" 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_us-gaap_InvestmentCompanyUnrealizedGainLossOnInvestmentPerShare_019e83f7-3513-7068-a971-80f52b5e7a01_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyUnrealizedGainLossOnInvestmentPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Change in Unrealized Gain (Loss) on Investments and Derivative Instruments (in USD per unit)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyUnrealizedGainLossOnInvestmentPerShare_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyUnrealizedGainLossOnInvestmentPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Unrealized Gain (Loss) on Investment, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyUnrealizedGainLossOnInvestmentPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyUnrealizedGainLossOnInvestmentPerShare"/>
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    <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_us-gaap_CommitmentsAndContingencies_019e83f7-3513-76d1-80bd-fb76f3211d3b_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 7)</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_bpef_OrganizationalCostReimbursementPeriod_019e83f7-3513-7fde-ba84-f12abe081b93_terseLabel_en-US" xlink:label="lab_bpef_OrganizationalCostReimbursementPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reimbursement period of organizational expenses</link:label>
    <link:label id="lab_bpef_OrganizationalCostReimbursementPeriod_label_en-US" xlink:label="lab_bpef_OrganizationalCostReimbursementPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organizational Cost, Reimbursement Period</link:label>
    <link:label id="lab_bpef_OrganizationalCostReimbursementPeriod_documentation_en-US" xlink:label="lab_bpef_OrganizationalCostReimbursementPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Organizational Cost, Reimbursement Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_OrganizationalCostReimbursementPeriod" xlink:href="bpef-20260630.xsd#bpef_OrganizationalCostReimbursementPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_OrganizationalCostReimbursementPeriod" xlink:to="lab_bpef_OrganizationalCostReimbursementPeriod" 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_bpef_MeasurementInputWeightedAverageCostOfCapitalMember_019e83f7-3513-71a2-831e-a91129661bc0_terseLabel_en-US" xlink:label="lab_bpef_MeasurementInputWeightedAverageCostOfCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">WACC</link:label>
    <link:label id="lab_bpef_MeasurementInputWeightedAverageCostOfCapitalMember_label_en-US" xlink:label="lab_bpef_MeasurementInputWeightedAverageCostOfCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Weighted Average Cost Of Capital [Member]</link:label>
    <link:label id="lab_bpef_MeasurementInputWeightedAverageCostOfCapitalMember_documentation_en-US" xlink:label="lab_bpef_MeasurementInputWeightedAverageCostOfCapitalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Weighted Average Cost Of Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_MeasurementInputWeightedAverageCostOfCapitalMember" xlink:href="bpef-20260630.xsd#bpef_MeasurementInputWeightedAverageCostOfCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_MeasurementInputWeightedAverageCostOfCapitalMember" xlink:to="lab_bpef_MeasurementInputWeightedAverageCostOfCapitalMember" 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_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_bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember_019e83f7-3514-7f86-ae39-434e4f59845e_terseLabel_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">High Water Mark Catch-Up</link:label>
    <link:label id="lab_bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember_label_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation - Incentive Rate, High Water Mark Catch-Up [Member]</link:label>
    <link:label id="lab_bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember_documentation_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation - Incentive Rate, High Water Mark Catch-Up</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember" xlink:href="bpef-20260630.xsd#bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember" xlink:to="lab_bpef_PerformanceParticipationAllocationIncentiveRateHighWaterMarkCatchUpMember" xlink:type="arc" order="1"/>
    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" 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_us-gaap_FairValueDisclosuresTextBlock_019e83f7-3514-77c1-ad6c-7f7927c58721_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">Investments and 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_bpef_AllocationOfRedemptionDiscount_019e83f7-3513-7ac9-b675-c338a57401c2_terseLabel_en-US" xlink:label="lab_bpef_AllocationOfRedemptionDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allocation of Redemption Discount</link:label>
    <link:label id="lab_bpef_AllocationOfRedemptionDiscount_019e83f7-3513-7088-97d5-d0638ef931ab_verboseLabel_en-US" xlink:label="lab_bpef_AllocationOfRedemptionDiscount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Redemption discount</link:label>
    <link:label id="lab_bpef_AllocationOfRedemptionDiscount_label_en-US" xlink:label="lab_bpef_AllocationOfRedemptionDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allocation Of Redemption Discount</link:label>
    <link:label id="lab_bpef_AllocationOfRedemptionDiscount_documentation_en-US" xlink:label="lab_bpef_AllocationOfRedemptionDiscount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allocation Of Redemption Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_AllocationOfRedemptionDiscount" xlink:href="bpef-20260630.xsd#bpef_AllocationOfRedemptionDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_AllocationOfRedemptionDiscount" xlink:to="lab_bpef_AllocationOfRedemptionDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019e83f7-3514-7878-b01e-92239c156348_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 III</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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_019e83f7-3513-7e0a-a0ac-5c5c30bef5f5_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 Disclosure of Non-Cash Financing 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_bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate_019e83f7-3513-7b0e-8846-7b1223481a82_terseLabel_en-US" xlink:label="lab_bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital Contributions on Purchases of Investments from Affiliates</link:label>
    <link:label id="lab_bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate_label_en-US" xlink:label="lab_bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Contribution On Purchase Of Investment From Affiliate</link:label>
    <link:label id="lab_bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate_documentation_en-US" xlink:label="lab_bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital Contribution On Purchase Of Investment From Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate" xlink:href="bpef-20260630.xsd#bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate" xlink:to="lab_bpef_CapitalContributionOnPurchaseOfInvestmentFromAffiliate" 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_srt_StatementGeographicalAxis_019e83f7-3513-73df-815f-8c9fe6136e00_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementGeographicalAxis" xlink:to="lab_srt_StatementGeographicalAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_RestOfWorldMember_019e83f7-35de-761c-983a-5b5346380904_terseLabel_en-US" xlink:label="lab_bpef_RestOfWorldMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rest of World</link:label>
    <link:label id="lab_bpef_RestOfWorldMember_label_en-US" xlink:label="lab_bpef_RestOfWorldMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rest Of World [Member]</link:label>
    <link:label id="lab_bpef_RestOfWorldMember_documentation_en-US" xlink:label="lab_bpef_RestOfWorldMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rest Of World</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_RestOfWorldMember" xlink:href="bpef-20260630.xsd#bpef_RestOfWorldMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_RestOfWorldMember" xlink:to="lab_bpef_RestOfWorldMember" 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_019e83f7-3514-7f40-80b1-7c83709eb95e_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:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" 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_us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration_019e83f7-3513-78c5-8898-1c57abe2e019_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liability, related party [extensible enumeration]</link:label>
    <link:label id="lab_us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liability, Related Party [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration" xlink:to="lab_us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayable_019e83f7-3513-755a-85d6-fba2b604993b_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Promissory Notes Payable</link:label>
    <link:label id="lab_us-gaap_NotesPayable_019e83f7-3513-70f8-8b78-a4d3a656684c_verboseLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Promissory note payable</link:label>
    <link:label id="lab_us-gaap_NotesPayable_label_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayable" xlink:to="lab_us-gaap_NotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_019e83f7-3513-782a-859a-cfb706afe0ed_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">Income 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_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e83f7-3513-74f2-aeb8-e942cc60664e_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, Beginning of Period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e83f7-3513-7297-928b-869459b9dfe3_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, 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_dei_EntityIncorporationStateCountryCode_019e83f7-3513-7859-8663-1531aa4a891b_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:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" 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_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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ManagementAndServiceFeesIncentiveRate_019e83f7-3513-7101-93cf-e893f3ad5696_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 rate (as percent)</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>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <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_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_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_019e83f7-35de-75f6-84db-b8f5d5f6160a_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019e83f7-3513-7188-afa8-78e59f3a4851_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:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" 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_LimitedPartnersCapitalAccount_019e83f7-3513-7aea-bfe1-49b956d90288_terseLabel_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Limited Partnership Unit</link:label>
    <link:label id="lab_us-gaap_LimitedPartnersCapitalAccount_label_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Limited Partners' Capital Account</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LimitedPartnersCapitalAccount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedPartnersCapitalAccount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LimitedPartnersCapitalAccount" xlink:to="lab_us-gaap_LimitedPartnersCapitalAccount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalUnitsMember_019e83f7-3514-7bfa-842a-e0372488858d_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital Units</link:label>
    <link:label id="lab_us-gaap_CapitalUnitsMember_label_en-US" xlink:label="lab_us-gaap_CapitalUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Units [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalUnitsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CapitalUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalUnitsMember" xlink:to="lab_us-gaap_CapitalUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum_019fd918-39ab-7832-9ee0-b739d048e8d4_terseLabel_en-US" xlink:label="lab_bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan to value ratio</link:label>
    <link:label id="lab_bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum_label_en-US" xlink:label="lab_bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Covenant, Loan To Value Ratio, Maximum</link:label>
    <link:label id="lab_bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum_documentation_en-US" xlink:label="lab_bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Covenant, Loan To Value Ratio, Maximum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum" xlink:href="bpef-20260630.xsd#bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum" xlink:to="lab_bpef_LineOfCreditFacilityCovenantLoanToValueRatioMaximum" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_019e83f7-3513-7114-962f-80f541e26f2e_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">Increase (Decrease) in 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_MeasurementInputTypeAxis_019e83f7-3513-70bd-ae79-ab739625fad5_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019e83f7-3513-7f4e-91de-90592c3ec7f0_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_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" 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"/>
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    <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>
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    <link:label id="lab_bpef_InvestmentIncomeInvestmentExpenseSubjectToExpenseSupport_documentation_en-US" xlink:label="lab_bpef_InvestmentIncomeInvestmentExpenseSubjectToExpenseSupport" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Income, Investment Expense, Subject To Expense Support</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentIncomeInvestmentExpenseSubjectToExpenseSupport" xlink:to="lab_bpef_InvestmentIncomeInvestmentExpenseSubjectToExpenseSupport" xlink:type="arc" order="1"/>
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    <link:label id="lab_currency_AllCurrenciesDomain_label_en-US" xlink:label="lab_currency_AllCurrenciesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Currencies [Domain]</link:label>
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    <link:label id="lab_bpef_IncreaseDecreaseInDeferredIncomeTaxLiability_documentation_en-US" xlink:label="lab_bpef_IncreaseDecreaseInDeferredIncomeTaxLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Deferred Income Tax Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_IncreaseDecreaseInDeferredIncomeTaxLiability" xlink:href="bpef-20260630.xsd#bpef_IncreaseDecreaseInDeferredIncomeTaxLiability"/>
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    <link:label id="lab_us-gaap_CapitalUnitsByClassAxis_label_en-US" xlink:label="lab_us-gaap_CapitalUnitsByClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Units by Class [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalUnitsByClassAxis" xlink:to="lab_us-gaap_CapitalUnitsByClassAxis" xlink:type="arc" order="1"/>
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    <link:label id="lab_dei_FormerAddressMember_label_en-US" xlink:label="lab_dei_FormerAddressMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Former Address [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDividendsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInDividendsReceivable"/>
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    <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>
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    <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_019e83f7-3513-779b-b724-186918bd5ddd_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">Purchase 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_us-gaap_EquitySecuritiesIndustryMember_019e83f7-3513-750c-8282-b5eb7f8aedcd_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_bpef_ServicingFeesMember_019e83f7-3514-7e36-97a3-b3a07acb7b75_terseLabel_en-US" xlink:label="lab_bpef_ServicingFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Fees</link:label>
    <link:label id="lab_bpef_ServicingFeesMember_label_en-US" xlink:label="lab_bpef_ServicingFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Fees [Member]</link:label>
    <link:label id="lab_bpef_ServicingFeesMember_documentation_en-US" xlink:label="lab_bpef_ServicingFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Servicing Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_ServicingFeesMember" xlink:href="bpef-20260630.xsd#bpef_ServicingFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_ServicingFeesMember" xlink:to="lab_bpef_ServicingFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_DirectorFeeAndOtherExpenses_019e83f7-3513-7b78-bdde-0e896e59f0a6_terseLabel_en-US" xlink:label="lab_bpef_DirectorFeeAndOtherExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Director fee and other expenses</link:label>
    <link:label id="lab_bpef_DirectorFeeAndOtherExpenses_label_en-US" xlink:label="lab_bpef_DirectorFeeAndOtherExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Director Fee And Other Expenses</link:label>
    <link:label id="lab_bpef_DirectorFeeAndOtherExpenses_documentation_en-US" xlink:label="lab_bpef_DirectorFeeAndOtherExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Director Fee And Other Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_DirectorFeeAndOtherExpenses" xlink:href="bpef-20260630.xsd#bpef_DirectorFeeAndOtherExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_DirectorFeeAndOtherExpenses" xlink:to="lab_bpef_DirectorFeeAndOtherExpenses" 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_019e83f7-3513-7bb1-8ec8-f9b3f00c17c8_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_bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract_019e83f7-3513-70d4-9221-427e0a31e793_terseLabel_en-US" xlink:label="lab_bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract" 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_bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments To Reconcile Net Assets From Operations To Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:label id="lab_bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract_documentation_en-US" xlink:label="lab_bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustments To Reconcile Net Assets From Operations To Cash Provided by (Used in) Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="bpef-20260630.xsd#bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_bpef_AdjustmentsToReconcileNetAssetsFromOperationsToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PartnersCapitalAccountSaleOfUnits_019e83f7-3513-7ad4-9e35-e8c218a08495_terseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountSaleOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from Units Issued</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountSaleOfUnits_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountSaleOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partners' Capital Account, Sale of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnersCapitalAccountSaleOfUnits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountSaleOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnersCapitalAccountSaleOfUnits" xlink:to="lab_us-gaap_PartnersCapitalAccountSaleOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019e83f7-3514-723b-ab19-ee4c005278a7_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 and Nonrelated Parties [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_us-gaap_InvestmentOwnedPercentOfNetAssets_019e83f7-3513-7a6e-9e2c-7214c89ce615_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 a Percentage 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_bpef_InvestmentOwnedCashAndDerivativeAssetFairValue_019e83f7-35de-7978-bc2f-f30c3f497312_totalLabel_en-US" xlink:label="lab_bpef_InvestmentOwnedCashAndDerivativeAssetFairValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_bpef_InvestmentOwnedCashAndDerivativeAssetFairValue_label_en-US" xlink:label="lab_bpef_InvestmentOwnedCashAndDerivativeAssetFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Cash And Derivative Asset, Fair Value</link:label>
    <link:label id="lab_bpef_InvestmentOwnedCashAndDerivativeAssetFairValue_documentation_en-US" xlink:label="lab_bpef_InvestmentOwnedCashAndDerivativeAssetFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Owned, Cash And Derivative Asset, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentOwnedCashAndDerivativeAssetFairValue" xlink:href="bpef-20260630.xsd#bpef_InvestmentOwnedCashAndDerivativeAssetFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentOwnedCashAndDerivativeAssetFairValue" xlink:to="lab_bpef_InvestmentOwnedCashAndDerivativeAssetFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentCompanyIncreaseDecreaseFromShareTransaction_019e83f7-3514-7ff2-8588-2285e68b727a_totalLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyIncreaseDecreaseFromShareTransaction" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Contributions for Units Issued</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyIncreaseDecreaseFromShareTransaction_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyIncreaseDecreaseFromShareTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Capital Share Transaction, Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyIncreaseDecreaseFromShareTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyIncreaseDecreaseFromShareTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyIncreaseDecreaseFromShareTransaction" xlink:to="lab_us-gaap_InvestmentCompanyIncreaseDecreaseFromShareTransaction" 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_PartnersCapitalAccountUnitsRedeemed_019e83f7-3513-7c42-ae3c-6a4e1204e41e_terseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountUnitsRedeemed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Units redeemed (in units)</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountUnitsRedeemed_019e83f7-3513-7dc7-875b-ed76c545fc42_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountUnitsRedeemed" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Units Redeemed (in units)</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountUnitsRedeemed_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountUnitsRedeemed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partners' Capital Account, Units, Redeemed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnersCapitalAccountUnitsRedeemed" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountUnitsRedeemed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnersCapitalAccountUnitsRedeemed" xlink:to="lab_us-gaap_PartnersCapitalAccountUnitsRedeemed" 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_019e83f7-3513-7898-87ec-472883ad5c18_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_us-gaap_InvestmentCompanyExpenseRatioExcludingIncentiveFee_019e83f7-3513-7333-a341-d13eeb44acb2_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyExpenseRatioExcludingIncentiveFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Expenses (as percent)</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyExpenseRatioExcludingIncentiveFee_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyExpenseRatioExcludingIncentiveFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Expense Ratio, after Fee Waiver and before Incentive Fee Deduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyExpenseRatioExcludingIncentiveFee" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyExpenseRatioExcludingIncentiveFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyExpenseRatioExcludingIncentiveFee" xlink:to="lab_us-gaap_InvestmentCompanyExpenseRatioExcludingIncentiveFee" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireInvestments_019e83f7-3513-7388-9d92-7f021c3dfcae_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payment for investment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireInvestments" 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_bpef_InvestmentCompanyRatioToAverageNetAssetsAbstract_019e83f7-3513-79b8-b871-c216f644753a_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ratios to Weighted-Average Net Assets</link:label>
    <link:label id="lab_bpef_InvestmentCompanyRatioToAverageNetAssetsAbstract_label_en-US" xlink:label="lab_bpef_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_bpef_InvestmentCompanyRatioToAverageNetAssetsAbstract_documentation_en-US" xlink:label="lab_bpef_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_bpef_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyRatioToAverageNetAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:to="lab_bpef_InvestmentCompanyRatioToAverageNetAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock_019e83f7-3514-79f4-88d2-7d6c47d13bef_terseLabel_en-US" xlink:label="lab_bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Realized and Unrealized Gain (Loss) on Investments</link:label>
    <link:label id="lab_bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Realized And Unrealized Gain (Loss) On Investments, Policy [Policy Text Block]</link:label>
    <link:label id="lab_bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Realized And Unrealized Gain (Loss) On Investments, Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock" xlink:href="bpef-20260630.xsd#bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock" xlink:to="lab_bpef_NetRealizedAndUnrealizedGainLossOnInvestmentsPolicyPolicyTextBlock" 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_bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins_019e83f7-3513-7130-86ca-9266bd7c01ab_terseLabel_en-US" xlink:label="lab_bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period before reimbursement begins (in months)</link:label>
    <link:label id="lab_bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins_label_en-US" xlink:label="lab_bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Related Parties, Period Before Reimbursement Begins</link:label>
    <link:label id="lab_bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins_documentation_en-US" xlink:label="lab_bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Liabilities, Related Parties, Period Before Reimbursement Begins</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins" xlink:href="bpef-20260630.xsd#bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins" xlink:to="lab_bpef_OtherLiabilitiesRelatedPartiesPeriodBeforeReimbursementBegins" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare_019e83f7-3514-79a3-9767-b829000877b5_terseLabel_en-US" xlink:label="lab_bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allocation of Capital Contributions on Purchases of Investments from Affiliates (in USD per unit)</link:label>
    <link:label id="lab_bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare_label_en-US" xlink:label="lab_bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Allocation Of Capital Contribution On Purchase Of Investment From Affiliate, Per Share</link:label>
    <link:label id="lab_bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare_documentation_en-US" xlink:label="lab_bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Company, Allocation Of Capital Contribution On Purchase Of Investment From Affiliate, Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare" xlink:href="bpef-20260630.xsd#bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare" xlink:to="lab_bpef_InvestmentCompanyAllocationOfCapitalContributionOnPurchaseOfInvestmentFromAffiliatePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_019e83f7-3513-7ba2-b706-8ddf6c79bc8f_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" 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_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_bpef_CapitalUnitClassB1Member_019e83f7-3513-7302-ad7d-62641379274f_terseLabel_en-US" xlink:label="lab_bpef_CapitalUnitClassB1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class B-1 Units</link:label>
    <link:label id="lab_bpef_CapitalUnitClassB1Member_019e83f7-3513-7303-870c-f711e31a2d00_verboseLabel_en-US" xlink:label="lab_bpef_CapitalUnitClassB1Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Class B-1 Units</link:label>
    <link:label id="lab_bpef_CapitalUnitClassB1Member_label_en-US" xlink:label="lab_bpef_CapitalUnitClassB1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Unit, Class B-1 [Member]</link:label>
    <link:label id="lab_bpef_CapitalUnitClassB1Member_documentation_en-US" xlink:label="lab_bpef_CapitalUnitClassB1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital Unit, Class B-1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_CapitalUnitClassB1Member" xlink:href="bpef-20260630.xsd#bpef_CapitalUnitClassB1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_CapitalUnitClassB1Member" xlink:to="lab_bpef_CapitalUnitClassB1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignExchangeForwardMember_019e83f7-3513-77da-b135-e29816a83fff_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_us-gaap_ScheduleOfStockByClassTextBlock_019e83f7-3513-7528-9935-b816a563394a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Transactions in Fund&#8217;s Units</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfStockByClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_019e83f7-3514-74e7-a9d3-069b00aaf045_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_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_bpef_PerformanceParticipationAllocationTotalReturnMember_019e83f7-3513-7b08-8ee9-accfce528e89_terseLabel_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationTotalReturnMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation, Total Return</link:label>
    <link:label id="lab_bpef_PerformanceParticipationAllocationTotalReturnMember_label_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationTotalReturnMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation, Total Return [Member]</link:label>
    <link:label id="lab_bpef_PerformanceParticipationAllocationTotalReturnMember_documentation_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationTotalReturnMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BPEF, Performance Participation Allocation, Total Return</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PerformanceParticipationAllocationTotalReturnMember" xlink:href="bpef-20260630.xsd#bpef_PerformanceParticipationAllocationTotalReturnMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PerformanceParticipationAllocationTotalReturnMember" xlink:to="lab_bpef_PerformanceParticipationAllocationTotalReturnMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments_019e83f7-3513-7b3f-bb28-8c9ab67ba7c3_terseLabel_en-US" xlink:label="lab_bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital Contribution on Purchase of Investment from Affiliate</link:label>
    <link:label id="lab_bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments_label_en-US" xlink:label="lab_bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments" 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, Capital Contribution On Purchase Of Investments</link:label>
    <link:label id="lab_bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments_documentation_en-US" xlink:label="lab_bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments" 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, Capital Contribution On Purchase Of Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments" xlink:href="bpef-20260630.xsd#bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments" xlink:to="lab_bpef_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetCapitalContributionOnPurchaseOfInvestments" 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_bpef_NumberOfClassesOfLimitedPartnershipUnits_019e83f7-3513-7919-9c12-f7668c40c6d0_terseLabel_en-US" xlink:label="lab_bpef_NumberOfClassesOfLimitedPartnershipUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of classes of limited partnership units</link:label>
    <link:label id="lab_bpef_NumberOfClassesOfLimitedPartnershipUnits_label_en-US" xlink:label="lab_bpef_NumberOfClassesOfLimitedPartnershipUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Classes Of Limited Partnership Units</link:label>
    <link:label id="lab_bpef_NumberOfClassesOfLimitedPartnershipUnits_documentation_en-US" xlink:label="lab_bpef_NumberOfClassesOfLimitedPartnershipUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Classes Of Limited Partnership Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_NumberOfClassesOfLimitedPartnershipUnits" xlink:href="bpef-20260630.xsd#bpef_NumberOfClassesOfLimitedPartnershipUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_NumberOfClassesOfLimitedPartnershipUnits" xlink:to="lab_bpef_NumberOfClassesOfLimitedPartnershipUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_019e83f7-3513-7711-b7e4-518ce8e68fb7_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" 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_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" 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_019e83f7-3513-703c-90bb-eaa13e7e0e01_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_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_us-gaap_InvestmentCompanyFinancialHighlightsTable_019e83f7-3513-7714-91dd-bb63466e2f4e_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyFinancialHighlightsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Highlights [Table]</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyFinancialHighlightsTable_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyFinancialHighlightsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Financial Highlights [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentCompanyFinancialHighlightsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentCompanyFinancialHighlightsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentCompanyFinancialHighlightsTable" xlink:to="lab_us-gaap_InvestmentCompanyFinancialHighlightsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019e83f7-3513-7dcf-a514-9aee230d0abb_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:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" 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_bpef_AdministrationFeeBelowNetAssetValueThreshold_019e83f7-3513-7909-8c40-43953a84a038_terseLabel_en-US" xlink:label="lab_bpef_AdministrationFeeBelowNetAssetValueThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administration fee charged when below net asset value threshold</link:label>
    <link:label id="lab_bpef_AdministrationFeeBelowNetAssetValueThreshold_label_en-US" xlink:label="lab_bpef_AdministrationFeeBelowNetAssetValueThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administration Fee, Below Net Asset Value Threshold</link:label>
    <link:label id="lab_bpef_AdministrationFeeBelowNetAssetValueThreshold_documentation_en-US" xlink:label="lab_bpef_AdministrationFeeBelowNetAssetValueThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Administration Fee, Below Net Asset Value Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_AdministrationFeeBelowNetAssetValueThreshold" xlink:href="bpef-20260630.xsd#bpef_AdministrationFeeBelowNetAssetValueThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_AdministrationFeeBelowNetAssetValueThreshold" xlink:to="lab_bpef_AdministrationFeeBelowNetAssetValueThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPeriod_019e83f7-3513-73f6-9bbc-ac93d1f97b20_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption period</link:label>
    <link:label id="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPeriod_label_en-US" xlink:label="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Investments, Entities that Calculate Net Asset Value Per Share, Redemption Restriction Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPeriod" xlink:to="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_019e83f7-3514-71a1-b924-c45b05512865_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" 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_bpef_PerformanceParticipationAllocationPolicyTextBlock_019e83f7-3513-7216-ae39-f9eb7b8ae182_terseLabel_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation</link:label>
    <link:label id="lab_bpef_PerformanceParticipationAllocationPolicyTextBlock_label_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation [Policy Text Block]</link:label>
    <link:label id="lab_bpef_PerformanceParticipationAllocationPolicyTextBlock_documentation_en-US" xlink:label="lab_bpef_PerformanceParticipationAllocationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance Participation Allocation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_PerformanceParticipationAllocationPolicyTextBlock" xlink:href="bpef-20260630.xsd#bpef_PerformanceParticipationAllocationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bpef_PerformanceParticipationAllocationPolicyTextBlock" xlink:to="lab_bpef_PerformanceParticipationAllocationPolicyTextBlock" 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_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilitiesPercentOfNetAssets_019e83f7-3513-7d19-b13e-ddc6c8ed8fd7_terseLabel_en-US" xlink:label="lab_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilitiesPercentOfNetAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities in Excess of Other Assets</link:label>
    <link:label id="lab_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilitiesPercentOfNetAssets_label_en-US" xlink:label="lab_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilitiesPercentOfNetAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninvestment Asset Less Noninvestment Liability, Percent of Net Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilitiesPercentOfNetAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilitiesPercentOfNetAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilitiesPercentOfNetAssets" xlink:to="lab_us-gaap_NonInvestmentAssetsLessNonInvestmentLiabilitiesPercentOfNetAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetInvestmentIncomeAbstract_019e83f7-3513-7472-b9ca-0e559df45bb8_terseLabel_en-US" xlink:label="lab_us-gaap_NetInvestmentIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income</link:label>
    <link:label id="lab_us-gaap_NetInvestmentIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_NetInvestmentIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Investment Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetInvestmentIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetInvestmentIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetInvestmentIncomeAbstract" xlink:to="lab_us-gaap_NetInvestmentIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList_019e83f7-3513-766e-9e00-43803782eef9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value, asset, recurring basis, unobservable input reconciliation, gain (loss), statement of income or comprehensive income</link:label>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList_label_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:to="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossInvestmentIncomeOperating_019e83f7-3513-7dc7-8983-a067b6ee1066_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 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_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_us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_019e83f7-3514-72bb-8fc8-20f1a686d90e_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</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_019e83f7-3513-7780-9d6a-c5fdc43f11c9_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:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
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    <link:label id="lab_srt_NorthAmericaMember_label_en-US" xlink:label="lab_srt_NorthAmericaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">North America [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_NorthAmericaMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_NorthAmericaMember"/>
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    <link:label id="lab_bpef_CapitalUnitClassB2Member_019e83f7-3513-7d41-986f-1a425212b07c_terseLabel_en-US" xlink:label="lab_bpef_CapitalUnitClassB2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class B-2 Units</link:label>
    <link:label id="lab_bpef_CapitalUnitClassB2Member_label_en-US" xlink:label="lab_bpef_CapitalUnitClassB2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Unit, Class B-2 [Member]</link:label>
    <link:label id="lab_bpef_CapitalUnitClassB2Member_documentation_en-US" xlink:label="lab_bpef_CapitalUnitClassB2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital Unit, Class B-2</link:label>
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    <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_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_us-gaap_ConsolidationPolicyTextBlock_019e83f7-3514-7008-936b-113fb6c83738_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">Principles of 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_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"/>
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    <link:label id="lab_us-gaap_NetIncomeLoss_019e83f7-3513-7410-acf8-e92ac79ed7e3_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_019e83f7-3513-73e4-a2a3-8007c33aadb2_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"/>
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    <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"/>
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    <link:label id="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPercentage_019e83f7-3513-7b65-a825-cc6cc6076b86_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemed at a blended discount to NAV (in percent)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareRedemptionRestrictionPercentage"/>
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    <link:label id="lab_bpef_InvestmentsOwnedNumberOfAdditionalInvestmentsAcquired_019e83f7-3513-7656-8bc4-be54bf2e0908_terseLabel_en-US" xlink:label="lab_bpef_InvestmentsOwnedNumberOfAdditionalInvestmentsAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of additional investments acquired</link:label>
    <link:label id="lab_bpef_InvestmentsOwnedNumberOfAdditionalInvestmentsAcquired_label_en-US" xlink:label="lab_bpef_InvestmentsOwnedNumberOfAdditionalInvestmentsAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments Owned, Number Of Additional Investments Acquired</link:label>
    <link:label id="lab_bpef_InvestmentsOwnedNumberOfAdditionalInvestmentsAcquired_documentation_en-US" xlink:label="lab_bpef_InvestmentsOwnedNumberOfAdditionalInvestmentsAcquired" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments Owned, Number Of Additional Investments Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_InvestmentsOwnedNumberOfAdditionalInvestmentsAcquired" xlink:href="bpef-20260630.xsd#bpef_InvestmentsOwnedNumberOfAdditionalInvestmentsAcquired"/>
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    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_019e83f7-3514-7ee4-a059-2011a6346910_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted Cash Flows</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
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    <link:label id="lab_us-gaap_StatementTable_019e83f7-3513-73fe-a4ce-489e50f499c0_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"/>
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    <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"/>
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    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_019e83f7-3513-7cca-9019-bc3b2f9b56c4_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from Promissory Note Payable</link:label>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_019ffc7e-c59b-73bb-88ba-9e041de1795e_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from promissory notes payable</link:label>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromNotesPayable"/>
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    <link:label id="lab_bpef_DeferredTaxLiabilitiesNetDifferenceOfCarryingAmountsAndTaxBasesOfAssets_019e83f7-3513-78c7-8ddb-8f4b2f529ad5_terseLabel_en-US" xlink:label="lab_bpef_DeferredTaxLiabilitiesNetDifferenceOfCarryingAmountsAndTaxBasesOfAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities, temporary differences between financial statement carrying amounts and tax bases of assets</link:label>
    <link:label id="lab_bpef_DeferredTaxLiabilitiesNetDifferenceOfCarryingAmountsAndTaxBasesOfAssets_label_en-US" xlink:label="lab_bpef_DeferredTaxLiabilitiesNetDifferenceOfCarryingAmountsAndTaxBasesOfAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Net, Difference Of Carrying Amounts And Tax Bases Of Assets</link:label>
    <link:label id="lab_bpef_DeferredTaxLiabilitiesNetDifferenceOfCarryingAmountsAndTaxBasesOfAssets_documentation_en-US" xlink:label="lab_bpef_DeferredTaxLiabilitiesNetDifferenceOfCarryingAmountsAndTaxBasesOfAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Net, Difference Of Carrying Amounts And Tax Bases Of Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bpef_DeferredTaxLiabilitiesNetDifferenceOfCarryingAmountsAndTaxBasesOfAssets" xlink:href="bpef-20260630.xsd#bpef_DeferredTaxLiabilitiesNetDifferenceOfCarryingAmountsAndTaxBasesOfAssets"/>
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