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          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory" xlink:label="dei_EntityFilerCategory"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain" xlink:label="us-gaap_DebtInstrumentNameDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionsProFormaIncomeLossFromContinuingOperationsBeforeChangesInAccountingAndExtraordinaryItemsNetOfTax" xlink:label="us-gaap_BusinessAcquisitionsProFormaIncomeLossFromContinuingOperationsBeforeChangesInAccountingAndExtraordinaryItemsNetOfTax"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable"/>
          <link:loc xlink:type="locator" xlink:href="btsg-20260630.xsd#btsg_AmedisysAndLHCBranchesAcquisitionMember" xlink:label="btsg_AmedisysAndLHCBranchesAcquisitionMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax"/>
          <link:loc xlink:type="locator" xlink:href="btsg-20260630.xsd#btsg_BasicEarningsLossPerShareAbstract" xlink:label="btsg_BasicEarningsLossPerShareAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionProFormaInformationAbstract" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationLineItems" xlink:label="dei_DocumentInformationLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract" xlink:label="us-gaap_SegmentReportingAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock"/>
          <link:loc xlink:type="locator" xlink:href="btsg-20260630.xsd#btsg_LcSublimitMember" xlink:label="btsg_LcSublimitMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode" xlink:label="dei_EntityAddressPostalZipCode"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract" xlink:label="us-gaap_StatementOfFinancialPositionAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeasePrincipalPayments" xlink:label="us-gaap_FinanceLeasePrincipalPayments"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber" xlink:label="dei_LocalPhoneNumber"/>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien credit agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrossProfit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gross Profit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrossProfit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gross profit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Liability Assumed, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Recognized Liability Assumed, Liability, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeDescriptionOfTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Description of Terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeDescriptionOfTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, description of terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accrued Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accrued Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Operating and Nonoperating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Discontinued Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">(Loss) income from discontinued operations, net of income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Carrying Value and Estimated Fair Values of Debt Obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Carrying Values and Estimated Fair Values of Debt Instruments [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Borrowings outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Line of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Line of Credit, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis spread on variable rate (as a percent)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Basis Spread on Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares outstanding - diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Repurchase of Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchase of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Purchase of remaining noncontrolling interest paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letter of Credit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letter of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax effect of net share settlement of equity awards, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Effect of Net Share Settlement of Equity Awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax effect of net share settlement of equity awards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwards_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Tax effect of net share settlement of equity awards, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesReceivableNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notes receivable noncurrent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesReceivableNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes Receivable Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesReceivableNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Notes receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derecognition of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derecognition Of Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Derecognition of redeemable noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentOfContingentConsiderationInExcessOfAcquisitionDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment of Contingent Consideration in Excess of Acquisition Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentOfContingentConsiderationInExcessOfAcquisitionDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment of contingent consideration in excess of acquisition date fair value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentOfContingentConsiderationInExcessOfAcquisitionDateFairValue_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payment of contingent consideration in excess of acquisition date fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed noncontrolling interests.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proforma revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired and Liability Assumed [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Consideration Paid for Acquisitions and Estimated Fair Value of Assets Acquired and Liabilities Assumed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldForSaleOrDisposedOfBySaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations, Held-for-Sale or Disposed of by Sale [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldForSaleOrDisposedOfBySaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CloudComputing_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cloud computing.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CloudComputing_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cloud Computing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CloudComputing_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cloud computing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Adjustment of redeemable noncontrolling interest to redemption amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment Of Redeemable Noncontrolling Interest To Redemption Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustment of redeemable noncontrolling interests to redemption amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Face Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Principal amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Tax Expense (Benefit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Income tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Income tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Excess tax benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillForeignCurrencyTranslationGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Foreign Currency Translation, Gain (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillForeignCurrencyTranslationGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units (RSUs) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">RSUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Segments [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross borrowing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Line of credit facility, maximum borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAcquiredFromAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Acquired from Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAcquiredFromAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash acquired from acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSold_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cost of Goods and Services Sold, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Product and Service Sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of goods and services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSold_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">TEU price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of Debt and Common Stock Price per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance of Debt and Common Stock Price per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total, Fair value per unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total, Fair value per unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment for (Proceeds from) Other Investing Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FinancingLeaseObligations_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Financing lease obligations.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FinancingLeaseObligations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FinancingLeaseObligations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing lease obligations assumed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExpensesNotAllocatedAtSegmentLevelAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expenses not allocated at segment level:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExpensesNotAllocatedAtSegmentLevelAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Expenses not Allocated at Segment Level [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExpensesNotAllocatedAtSegmentLevelAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Proceeds, Issuance of Shares, Share-Based Payment Arrangement, Including Option Exercised, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds, Issuance of Shares, Share-Based Payment Arrangement, Including Option Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from shares issued under share-based compensation plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Inventory, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicare A.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicare A [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicare A</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Medicare Part A</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Redeemable Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed redeemable noncontrolling interests.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income taxes, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Deferred Tax Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Services revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicare B.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicare B [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicare B</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Medicare Part B</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DilutedEarningsLossPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Diluted Earnings Loss Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DilutedEarningsLossPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Diluted earnings loss per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DilutedEarningsLossPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Diluted income (loss) per share attributable to common shareholders:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotionalAmountToHedgeCashFlowRiskOfVariability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notional Amount, to Hedge Cash Flow Risk of Variability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotionalAmountToHedgeCashFlowRiskOfVariability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notional amount, to hedge the cash flow risk of variability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotionalAmountToHedgeCashFlowRiskOfVariability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Notional amount, to hedge cash flow risk of variability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Loss per share - basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other assets gross.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Finite-Lived Intangible Assets, Net, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Finite-Lived Intangible Assets, Net, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, after Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total intangible assets, Net Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion Of Tangible Equity Units Into Common Stock, value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Conversion of tangible equity units into common stock, value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of tangible equity units into common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchases of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwardsValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Effect of Net Share Settlement of Equity Awards Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwardsValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax effect of net share settlement of equity awards value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwardsValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax effect of net share settlement of equity awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScottGreenwellMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Scott Greenwell [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScottGreenwellMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Scott greenwell.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Tax Effect of Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax (benefit) expense of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB5TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche B 5 Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB5TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche B 5 term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB5TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranche B- 5 Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Income (Loss) from Discontinued Operation, Net of Tax, Per Basic Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income , net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other comprehensive income (loss), net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Other comprehensive income (loss) , net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Stated Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Principal at issuance (as a percent)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units Text Block</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tangible Equity Units ("TEUs")</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrivateAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Private and Other.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrivateAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private and Other [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrivateAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Private and Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentySixAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026 Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentySixAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Six Acquisition [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentySixAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty six acquisition.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Goodwill, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Goodwill, Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Goodwill, Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, $0.01 par value, 250,000,000 authorized, no shares issued and outstanding at June 30, 2026 and December 31, 2025</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineLoansMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Swingline loans.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineLoansMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Swingline Loans [member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineLoansMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Swingline Loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Repurchase of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repurchase of shares of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repurchases of shares of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Stock Options Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NontradeReceivablesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Nontrade Receivables, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NontradeReceivablesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nontrade Receivables, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NontradeReceivablesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-trade receivables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total notional value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Notional Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Derivative, notional amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accumulated Depreciation Of Property, Plant, And Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, accumulated depreciation of property, plant, and equipment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock issued in connection with acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Effective tax rate recognized in the statements of operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterestNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derecognition of redeemable noncontrolling interest, net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterestNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derecognition Of Redeemable Noncontrolling Interest, Net Of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterestNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Derecognition Of Redeemable Noncontrolling Interest, Net Of Tax.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Products</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsGrossExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Intangible Assets, Gross (Excluding Goodwill), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsGrossExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Excluding Goodwill, before Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsGrossExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total intangible assets, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsAmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units Amortizing Notes [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsAmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units amortizing notes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsAmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortizing Notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicare C</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicare C [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicare C.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Medicare Part C</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IndefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Indefinite Lived Licenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IndefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indefinite Lived Licenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IndefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Licenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IndefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Indefinite-lived Licenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidTaxes_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeGainLossReclassifiedToEarningsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Cash Flow Hedge Gain (Loss) Reclassified to Earnings, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeGainLossReclassifiedToEarningsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Relationships [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer Relationships</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Revenue by Payor Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Instrument, Periodic Payment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Periodic Payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">TEU installment payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Segment Reporting Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from (Repayments of) Lines of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayments of the Revolving Credit Facility, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDilutedAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDilutedAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Diluted income (loss) per share attributable to common shareholders:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Equity, Attributable to Parent, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Equity, Attributable to Parent, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total shareholders'' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of tangible equity units into common stock, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion Of Tangible Equity Units Into Common Stock,Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Conversion of tangible equity units into common stock,share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentConvertibleCashInstallmentPerUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument convertible cash installment per unit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentConvertibleCashInstallmentPerUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Convertible Cash Installment Per Unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentConvertibleCashInstallmentPerUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash installment per unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExistingContractsInterestRateSwapAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Existing Contracts Interest Rate Swap Agreements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExistingContractsInterestRateSwapAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Existing contracts interest rate swap agreements.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExistingContractsInterestRateSwapAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Existing contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under financing leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Current Portion of Obligations under Financing Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Current Portion of Obligations under Financing Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MorganStanleyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Morgan Stanley Member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MorganStanleyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Morgan Stanley [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MorganStanleyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Morgan Stanley</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Earnings Per Share ("EPS")</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeFixedInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Fixed Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeFixedInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fixed rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Income (Loss) from Discontinued Operation, Net of Tax, Per Diluted Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue Benchmark [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis of Accounting, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermNotesPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes Payable, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermNotesPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Notes Payable, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermNotesPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term portion of the amortizing notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total debt, net of debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock, Class of Stock [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Long-term debt repayments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Repayments of Long-Term Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repayments of Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayment of borrowings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed accrued expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Accrued Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revolving Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrual for Taxes Other than Income Taxes, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Taxes other than income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definite-lived Licenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Definite-lived licenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Definite-lived Licenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MarchTwoThousandTwentySixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">March Two Thousand Twenty Six Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MarchTwoThousandTwentySixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">March two thousand twenty six offering.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MarchTwoThousandTwentySixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">March 2026 Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForLoanLossesExpensed_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Credit Loss, Expense (Reversal)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForLoanLossesExpensed_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provision for credit losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Extinguishment of Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Extinguishment of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss on debt extinguishment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss on extinguishment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Costs of Goods Sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceReceivableForMalpracticeNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Insurance Receivable for Malpractice, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceReceivableForMalpracticeNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Insurance recoveries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, $0.01 par value, 1,500,000,000 shares authorized, 197,509,491 and 192,124,125 shares issued and outstanding at June 30, 2026 and December 31, 2025, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Basic and Diluted Net Income Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Gross Profit (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gross profit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedChecksInExcessOfCashBalanceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of obligations incurred and payable for accrued checks in excess of cash balance current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedChecksInExcessOfCashBalanceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Checks In Excess Of Cash Balance Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedChecksInExcessOfCashBalanceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Checks in excess of cash balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation and Amortization Expenses not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Depreciation and amortization expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Groups, Including Discontinued Operations [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of the Reconciles the Gross Proceeds With the Gain on Sale, Net of Tax for the Sale, the Financial Results, Aggregate Carrying Amounts of Assets and Liabilities Held for Sale and Significant Non-cash Items and Purchases of Property and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Intangible Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets, net of accumulated amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Noncash Income (Expense), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Noncash Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductOrServiceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) On Disposition Of Real Estate Discontinued Operations, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Gain (loss) on disposition of real estate discontinued operations, net.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retained earnings (accumulated deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long-term liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Long-Term Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 3</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Significant Unobservable Inputs (Level 3)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodValues_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Share repurchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodValues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchased During Period Values</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodValues_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock repurchased during period values.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion of Stock, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Mandatory conversion to common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash flows from discontinued operations investing activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash flows from discontinued operations investing activities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows used in investing activities of discontinued operations:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AlternateBaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Alternate base rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AlternateBaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Alternate Base Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AlternateBaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ABR</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in operating assets and liabilities, net of acquisitions and dispositions:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Impaired, Accumulated Impairment Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net of accumulated impairment losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPerShareWeightedAveragePriceOfSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Per Share Weighted Average Price of Shares Purchased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPerShareWeightedAveragePriceOfSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">VWAP of BTSG Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPerShareWeightedAveragePriceOfSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Average applicable market value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock on initial public offering, net, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WorkersCompensationLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Workers' Compensation Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WorkersCompensationLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Workers compensation insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Comprehensive income (loss) attributable to noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income (loss), net of tax:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Liabilities, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income taxes, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Amounts reclassified to earnings, net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Branches Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of branches acquired.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of branches acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">IPO [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Initial Public Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accounts, Notes and Loans Receivable, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable, net of allowance for credit losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definite-lived assets, Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant, and Equipment, Accumulated Depreciation, Depletion, and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net of accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SummaryOfSignificantAccountingPolicyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of significant accounting policy.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SummaryOfSignificantAccountingPolicyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary Of Significant Accounting Policy [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: Net loss attributable to noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Net of Tax, Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Net loss attributable to noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, Acquired, Weighted-Average Amortization Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definite-lived intangible assets estimated weighted average useful life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Indefinite-Lived, Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Line of credit facility, remaining borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsIssuedDuringPeriodNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible Equity Units Issued During Period New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsIssuedDuringPeriodNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units Issued During Period New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsIssuedDuringPeriodNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tangible equity unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_JuneTwoThousandTwentySixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">June 2026 Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_JuneTwoThousandTwentySixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">June Two Thousand Twenty Six Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_JuneTwoThousandTwentySixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">June two thousand twenty six offering.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income from continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income from continuing operations, net of income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IncomeTaxExpenseBenefitExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Expense (Benefit) Expenses not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IncomeTaxExpenseBenefitExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income tax expense (benefit) expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IncomeTaxExpenseBenefitExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOther_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOther_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LcFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">LC facility member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LcFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">LC Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LcFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LC Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities, redeemable noncontrolling interests, and equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfIntangibleAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Intangible Assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfIntangibleAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Intangible Assets [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Liability, Classified, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Compensation Liability, Classified, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Deferred compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income (loss) from continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income from continuing operations attributable to common shareholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillPurchaseAccountingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement period adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillPurchaseAccountingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Measurement Period Adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Income (Loss) from Discontinued Operation, before Income Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income from discontinued operations, net of income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">(Loss) income of discontinued operations before incomes taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Insurance, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Health insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Depletion and Amortization, Nonproduction, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Depletion and Amortization, Nonproduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Businesses, Net of Cash Acquired, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Net of Cash Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquisitions of businesses, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Acquisitions of businesses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LettersOfCreditOutstandingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letters of Credit Outstanding, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LettersOfCreditOutstandingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letter of credit outstanding amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), after Reclassification and Tax [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flow hedges:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Earnings per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings per Share [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedGeneralAndProfessionalLiabilityInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of obligations incurred and payable for accrued general and professional liability insurance reserves current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedGeneralAndProfessionalLiabilityInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued General And Professional Liability Insurance Reserves Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedGeneralAndProfessionalLiabilityInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and professional liability insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Life (years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Notes Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Short-term portion of the amortizing notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net decrease in cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net increase in cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedLegalSettlementsAndProfessionalFeesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of obligations incurred through that date and payable accrued legal settlements and professional fees current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedLegalSettlementsAndProfessionalFeesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Legal Settlements And Professional Fees Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedLegalSettlementsAndProfessionalFeesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Legal settlements and professional fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MizuhoCapitalMarketsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Mizuho Capital Markets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MizuhoCapitalMarketsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Mizuho Capital Markets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MizuhoCapitalMarketsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mizuho Capital Markets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock repurchased during period share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodShare_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Share repurchase, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Operating Lease Right-of-Use Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Operating Lease Right-of-Use Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommonStockSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock shares purchased from underwriter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommonStockSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Shares Purchased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommonStockSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock shares purchased.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Inventories, Total</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumAmountOutstandingDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Amount Outstanding During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumAmountOutstandingDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate amount of outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfBusinessesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Number of Businesses Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfBusinessesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of businesses acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MaterialReconcilingItemsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Reconciling Item, Excluding Corporate Nonsegment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MaterialReconcilingItemsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Material Reconciling Items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax effects of net change in fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion of Stock, Shares Converted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Units converted at holder's option</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed operating lease right-of-use assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Operating Lease Right-of-use Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Unaudited Pro Forma Consolidated Financial Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Finite-Lived Intangible Assets, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, before Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definite-lived assets, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockIncludingAdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Including Additional Paid in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockIncludingAdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-In Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shareholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares outstanding - basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Per Diluted Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Gain (Loss) from Disposal of Discontinued Operation, before Income Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">(Loss) gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GeneralAndProfessionalLiabilityInsuranceReservesLongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of general and professional liability insurance reserves long-term liabilities, noncurrent (with maturities initially due after one year or beyond the operating cycle if longer), excluding current portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GeneralAndProfessionalLiabilityInsuranceReservesLongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General And Professional Liability Insurance Reserves Long-term Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GeneralAndProfessionalLiabilityInsuranceReservesLongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and professional liability insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfProductInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nature of Operation, Product Information, Concentration of Risk [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued for payment of acquisition, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Accrued Liabilities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Line of credit facility, maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SummaryOfSignificantAccountingPolicyLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of significant accounting policy.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SummaryOfSignificantAccountingPolicyLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary Of Significant Accounting Policy [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset and Goodwill [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Withheld Related To Net Share Settlement Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Shares withheld related to net share settlement value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares withheld related to net share settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLongTermInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLongTermInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Long-Term Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Significant Other Observable Inputs (Level 2)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationRevenueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Revenue [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationRevenueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reconciliation of income:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfCustomer_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of Customer.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfCustomer_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfCustomer_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of customer whose revenue was 10% or more of consolidated revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of interest rate swaps liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Cash Flow Hedge Liability at Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pharmacy Solutions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pharmacy Solutions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pharmacy Solutions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Loss per share - diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock , par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income attributable to BrightSpring Health Services, Inc. and subsidiaries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Impairment, Long-Lived Asset, Held-for-Use, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Asset, Held and Used, Impairment Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of long-lived assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued under share-based compensation plan, including tax effects</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ChangeInFairValueOfContingentConsiderationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Change in fair value of contingent considerations net.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ChangeInFairValueOfContingentConsiderationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in fair value of contingent consideration, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ChangeInFairValueOfContingentConsiderationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Fair Value of Contingent Considerations Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash receivable for the disposal including discontinued operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Disposition of Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss (gain) on disposition of fixed assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Current Portion of Obligations under Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Current Portion of Obligations under Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalBalanceSheetDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Balance Sheet Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalBalanceSheetDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Detail of Certain Balance Sheet Accounts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsPurchaseContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units Purchase Contracts [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsPurchaseContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units purchase contracts.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsPurchaseContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase Contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Comprehensive income attributable to BrightSpring Health Services, Inc. and subsidiaries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency translation adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total debt instruments, fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Instrument, Fair Value Disclosure, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revolving Credit Loans - Payable To Lenders At Sofr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving Credit Loans - Payable to Lenders at SOFR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Revolving credit loans - payable to lenders at SOFR plus applicable margin member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Excluding Goodwill, after Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets, net of accumulated amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total intangible assets, Net Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Intangible assets, net of accumulated amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock for settlement of RSUs, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Restricted Stock Award, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under financing leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LossOnExtinguishmentOfDebtExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss on extinguishment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LossOnExtinguishmentOfDebtExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss on Extinguishment of Debt Expenses not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LossOnExtinguishmentOfDebtExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Loss on extinguishment of debt expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of long-term liabilities automobile insurance reserves, noncurrent (with maturities initially due after one year or beyond the operating cycle if longer), excluding current portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Liabilities Automobile Insurance Reserves, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Automobile insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost of services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RelatedPartyTransactionsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RelatedPartyTransactionsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disclosure of accounting policy for related party transactions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RelatedPartyTransactionsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DuesAndSubscriptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dues And Subscriptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DuesAndSubscriptions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Dues and subscriptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DuesAndSubscriptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dues and subscriptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentFloorRate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument floor rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentFloorRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Floor Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentFloorRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, floor rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Contract [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Potentially dilutive common share equivalents excluded from the computation of diluted net income (loss) per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Comprehensive income (loss), net of tax, attributable to redeemable noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income Loss Attributable To Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Comprehensive (loss) income attributable to redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Comprehensive loss attributable to redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive (Loss) Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable, Trade</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Inventory, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Inventory, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfGoods_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost of goods.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfGoods_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of goods</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Property, Plant, and Equipment, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net of accumulated depreciation of $104,314</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentsForUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net of underwriting discounts and commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentsForUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net of underwriting fees and offering costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentsForUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payments for underwriting discounts and commissions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentsForUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments For Underwriting Discounts And Commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Debt, Current Maturities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Less: current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CertainPostClosingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Certain Post closing Adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CertainPostClosingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Certain post closing adjustments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CertainPostClosingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: certain post-closing adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DirectCostsToSell_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Direct Costs To Sell</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DirectCostsToSell_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Direct costs to sell.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DirectCostsToSell_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: direct costs to sell</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under financing leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Current Portion Of Obligations Under Financing Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Current Portion Of Obligations Under Financing Leases.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operations [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities, Redeemable Noncontrolling Interests, and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Other Operating Assets and Liabilities, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Operating Assets and Liabilities, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets and liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other assets and liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Acquired During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill added through acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensatedAbsencesLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Compensated Absences Liability, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensatedAbsencesLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Compensated Absences Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensatedAbsencesLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Compensated absences</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Obligations under Operating Leases, Net of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Obligations under Operating Leases, Net of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under operating leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Intangible Assets, Other than Goodwill, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Agricole Corporate And Investment Bank One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Credit agricole corporate and investment bank one.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Agricole Corporate and Investment Bank</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupClassificationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Classification [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ServiceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Service [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ServiceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Securities Act File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentyFiveAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Five Acquisition [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentyFiveAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty five acquisition.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentyFiveAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2025 Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WorkersCompensationLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Workers' Compensation Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WorkersCompensationLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Workers compensation insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExtinguishmentOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Extinguishment of redeemable noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExtinguishmentOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Extinguishment Of Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExtinguishmentOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Extinguishment of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExtinguishmentOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Extinguishment of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">(Accumulated Deficit) Retained Earnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Diluted Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Diluted Share, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-tax gain on sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Real Estate, Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Other Asset, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Policies [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net (loss) income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Selling, General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, general, and administrative expenses not allocated at segment level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trade Names [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade Names</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Income (Loss) Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net (loss) income attributable to redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net loss attributable to noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss attributable to noncontrolling interests included in continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of stock options, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Receivable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ProfitLossExcludingRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Profit Loss Excluding Redeemable Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ProfitLossExcludingRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Profit (loss) excluding redeemable noncontrolling interests.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ProfitLossExcludingRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ProfitLossExcludingRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfIntangibleAssetsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Intangible Assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfIntangibleAssetsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Intangible Assets [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segments [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information, Pro Forma Income (Loss), after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income from continuing operations attributable to BrightSpring Health Services, Inc. and subsidiaries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfDrugs_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of drugs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfDrugs_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Drugs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfDrugs_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost of drugs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents included in assets held for sale at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Divestiture of Businesses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definitive agreement for cash proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Information [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental disclosures of cash flow information:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvancesOnInventoryPurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Advances on Inventory Purchases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvancesOnInventoryPurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventory returns receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisition Cost Of Acquired Entity Transaction Costs 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business acquisition cost of acquired entity transaction costs 1.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Excluding Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term debt, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total long-term debt, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Temporary Equity, Carrying Amount, Including Portion Attributable to Noncontrolling Interests, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Temporary Equity, Carrying Amount, Including Portion Attributable to Noncontrolling Interests, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Temporary Equity, Carrying Amount, Including Portion Attributable to Noncontrolling Interests, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Including Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestRateSwapsNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate swaps</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestRateSwapsNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swaps Non-current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestRateSwapsNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest rate swaps non-current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment depreciation and amortization expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation And Amortization Expense From Reportable Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Depreciation and amortization expense from reportable segment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Receivable, after Allowance for Credit Loss, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable, net of allowance for credit losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Wages and payroll taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Total Outstanding Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOtherShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity, Other Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOtherShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicaidMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicaid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicaidMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicaid.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicaidMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicaid [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income per common share (Note 10):</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CarryingAmountOfCommunityLivingBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Carrying Amount Of Community Living Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CarryingAmountOfCommunityLivingBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying amount of community living business.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CarryingAmountOfCommunityLivingBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: carrying amount of Community Living business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionNumberOfBranches_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisition Number Of Branches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionNumberOfBranches_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business acquisition number of branches.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionNumberOfBranches_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of branches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoanTrancheB6PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Incremental Term Loan Tranche B 6 Payable to Lenders at Sofr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoanTrancheB6PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien incremental term loan tranche B 6 payable to lenders at SOFR plus applicable margin.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoanTrancheB6PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Incremental Term Loan Tranche B-6 - Payable to Lenders at SOFR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductsAndServicesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Credit Agricole Corporate And Investment Bank Member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Agricole Corporate And Investment Bank [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Agricole Corporate and Investment Bank</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherDirectCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Direct Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherDirectCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other direct costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherDirectCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other direct costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsBeforeInterestIncomeTaxesDepreciationAndAmortizationFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Earnings before interest income taxes depreciation and amortization from reportable segment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsBeforeInterestIncomeTaxesDepreciationAndAmortizationFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Before Interest Income Taxes Depreciation And Amortization From Reportable Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsBeforeInterestIncomeTaxesDepreciationAndAmortizationFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment EBITDA</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsBeforeInterestIncomeTaxesDepreciationAndAmortizationFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total Segment EBITDA</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DeferredIncomeTaxesExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Taxes Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DeferredIncomeTaxesExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred income taxes expense (benefit).</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DeferredIncomeTaxesExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income taxes, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherPrepaidExpensesAndCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other prepaid expenses and current assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherPrepaidExpensesAndCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Prepaid Expenses and Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherPrepaidExpensesAndCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other prepaid expenses and current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Indefinite-Lived, Class [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedPropertyInsuranceReserves_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Property Insurance Reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedPropertyInsuranceReserves_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued property insurance reserves.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedPropertyInsuranceReserves_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConsiderationForPurchaseOfRedeemableNoncontrollingInterestInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Consideration for purchase of redeemable noncontrolling interest in accounts payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConsiderationForPurchaseOfRedeemableNoncontrollingInterestInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consideration For Purchase Of Redeemable Noncontrolling Interest In Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConsiderationForPurchaseOfRedeemableNoncontrollingInterestInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consideration for purchase of redeemable noncontrolling interest in accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under financing leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Obligations Under Financing Leases, Net Of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Obligations Under Financing Leases, Net Of Current Portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Indefinite-Lived Intangible Assets (Excluding Goodwill), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Indefinite-Lived Intangible Assets (Excluding Goodwill), Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Indefinite-Lived Intangible Assets (Excluding Goodwill), Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Excluding Goodwill, Indefinite-Lived</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Indefinite-lived assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Selling, general and administrative expense not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling General and Administrative Expense Not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total comprehensive income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Gain (Loss) on Disposal of Discontinued Operation, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Discontinued Operation, Gain (Loss) on Disposal of Discontinued Operation, Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capital Expenditures Incurred but Not yet Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchases of property and equipment in accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ForwardStartingContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Forward starting contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ForwardStartingContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Forward Starting Contracts [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ForwardStartingContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Forward Starting Contracts [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Taxes Paid, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Paid, after Refund Received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income taxes, net of refunds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock on initial public offering, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Interest Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segments [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeAssetAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Cash Flow Hedge Asset at Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeAssetAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of interest rate swaps asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Common Stock, Shares Outstanding (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInterestRateCashFlowHedgesPretaxAccumulatedOtherComprehensiveIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrealized Gain (Loss) on Interest Rate Cash Flow Hedges, Pretax, Accumulated Other Comprehensive Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInterestRateCashFlowHedgesPretaxAccumulatedOtherComprehensiveIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-tax gains</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RebateReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Rebate receivable current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RebateReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rebate receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deposits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset and Goodwill [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill and Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed current portion of obligations under operating leases.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Current Portion Of Obligations Under Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted average shares outstanding:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Denominator:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesPayableAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notes payable and other.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesPayableAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes Payable and Other [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesPayableAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Notes Payable and Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Tax Credit, Foreign, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Goodwill, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash flows from discontinued operations operating activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash flows from discontinued operations operating activities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from operating activities of discontinued operations:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Revenue, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Revenue, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of Aggregate Annual Quarterly Cash Installments Equivalent Per Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of Aggregate Annual Quarterly Cash Installments Equivalent Per Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of aggregate annual quarterly cash installments equivalent per year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income from continuing operations before income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestExpenseNetExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestExpenseNetExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Net Expenses not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestExpenseNetExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest expense, net expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by (used in) investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Operating Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating income of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating (loss) income of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Basic Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Basic Share, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfOtherAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Other Assets [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfOtherAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsPrepaidExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Prepaid Expense and Other Asset, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsPrepaidExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Groups, Including Discontinued Operations [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureTextBlockSupplementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disclosure Text Block Supplement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LicensingAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Licensing Agreements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LicensingAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Licenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentDelayedDraw_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument, delayed draw.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentDelayedDraw_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Delayed Draw</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentDelayedDraw_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Delayed draw</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RepurchasesOfCommonStockInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Repurchases of common stock in accounts payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RepurchasesOfCommonStockInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repurchases Of Common Stock In Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RepurchasesOfCommonStockInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repurchases of common stock in accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Principles of Consolidation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationOtherReconcilingItemsPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Other Reconciling Items, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationOtherReconcilingItemsPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discrete items recognized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityInitiationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Initiation Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityInitiationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Line of credit facility, agreement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldforsaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operation held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldforsaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations, Held-for-Sale [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SecondLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Second lien credit agreement member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SecondLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Second Lien Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SecondLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Second Lien Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Taxes paid related to net share settlement of equity awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment, Tax Withholding, Share-Based Payment Arrangement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasicAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasicAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basic income (loss) per share attributable to common shareholders:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortization of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of deferred debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Issuance Costs, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: debt issuance costs, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under financing leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Restricted Stock Award, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock for settlement of RSUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIntangibleAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Intangible Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Shares, Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Shares, Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Obligations under Financing Leases, Net of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Obligations under Financing Leases, Net of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under financing leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Comprehensive Income [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Purchase of Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from stock purchase contract issued under tangible equity units, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business Acquisition [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Consideration transferred to asset acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Aggregate purchase price, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of long-term liabilities noncurrent (with maturities initially due after one year or beyond the operating cycle if longer), excluding current portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Liabilities Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under operating leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax effects of amounts reclassified to earnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareDMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicare D.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareDMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicare D [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareDMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicare D</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareDMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Medicare Part D</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital, Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling General and Administrative Expense From Reportable Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Selling general and administrative expense from reportable segment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Revenues, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Products revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recently Adopted and Issued Accounting Standards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Recently Adopted Accounting Standards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CovenantsNotToCompleteMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Covenants Not to Complete.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CovenantsNotToCompleteMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Covenants Not to Complete [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CovenantsNotToCompleteMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Covenants Not to Complete</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Changes to Goodwill, by Reportable Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Derivative Instruments [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Interest Rate Swap with Notional Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk, Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">% of Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">SOFR</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents included in continuing operations at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and cash equivalents included in continuing operations at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedAutomobileInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying Value As Of The Balance Sheet Date Of Obligations Incurred And Payable For Accrued Automobile Insurance Reserves Current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedAutomobileInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Automobile Insurance Reserves Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedAutomobileInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Automobile insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares withheld related to net share settlement, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Withheld Related To Net Share Settlement, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementShares_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Shares withheld related to net share settlement, shares.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NetLossExcludingAllocableRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net loss excluding allocable redeemable noncontrolling interests.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NetLossExcludingAllocableRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Loss Excluding Allocable Redeemable Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NetLossExcludingAllocableRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss excluding allocable redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: current and deferred tax impact</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current and Deferred Tax Impact on Real Estate Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Current and deferred tax impact on real estate discontinued operations.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EffectiveIncomeTaxRateReconciliationExpectedPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Expected Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EffectiveIncomeTaxRateReconciliationExpectedPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Effective income tax rate reconciliation, expected percent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EffectiveIncomeTaxRateReconciliationExpectedPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated annual effective tax rate before discrete items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationPlanAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Plan Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationPlanAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSalesOfBusinessAffiliateAndProductiveAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSalesOfBusinessAffiliateAndProductiveAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Sales of Business, Affiliate and Productive Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineBaseRatePayableToLendersAtAbrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Swingline/base Rate - Payable To Lenders At Abr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineBaseRatePayableToLendersAtAbrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Swingline/Base Rate - Payable to Lenders at ABR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineBaseRatePayableToLendersAtAbrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Swingline/base rate - payable to lenders at ABR plus applicable margin member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommercialInsuranceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commercial Insurance.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommercialInsuranceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Insurance [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommercialInsuranceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial Insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpenditureDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capital Expenditure, Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpenditureDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchases of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure and Derivative Financial Instruments [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt and Derivatives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt disclosure and derivative financial instruments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Earnings per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Per Basic Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Term Loan[Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First Lien Term Loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">TEUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">6.75% Tangible Equity Unit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Six Point Seven Five Percentage Tangible Equity Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Prepaid and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and cash equivalents included in continuing operations at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesToBeAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of branches to be acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesToBeAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Branches To Be Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesToBeAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of branches to be acquired.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DoctorPayorNetworkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Doctor Payor Network.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DoctorPayorNetworkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Doctor Payor Network [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DoctorPayorNetworkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Doctor/Payor Network</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB6TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche B 6 Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB6TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche B 6 term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB6TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranche B-6 Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Emerging Growth Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Emerging Growth Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Prepaid Expenses and Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesIssuedInConnectionWithAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes issued in connection with acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesIssuedInConnectionWithAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notes issued in connection with acquisitions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesIssuedInConnectionWithAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Notes issued in connection with acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Shares issued for payment of acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued under share-based compensation plan, including tax effects, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amortizing notes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortizing Notes [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortizing Notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupClassificationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Classification [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental schedule of non-cash investing and financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less) [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed obligations under operating leases, net of current portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Obligations Under Operating Leases, Net Of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under operating leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Equity, Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Equity, Attributable to Noncontrolling Interest, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Equity, Attributable to Noncontrolling Interest, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Other Comprehensive Income (Loss), Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated other comprehensive income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">(Loss) income from discontinued operations, net of income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net (loss) income from discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, Amortization Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued for payment of acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Payment Arrangement, Noncash Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Noncash Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net income to net cash provided by operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and Cash Equivalents, at Carrying Value, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments of debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SeniorAmortizingNoteMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Senior Amortizing Note [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SeniorAmortizingNoteMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Senior Amortizing Note [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SeniorAmortizingNoteMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Senior Amortizing Note</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommunityLivingBusinessMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Community Living Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommunityLivingBusinessMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Community Living Business [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommunityLivingBusinessMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Community Living Business.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoanTrancheB5PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Incremental Term Loan Tranche B 5 Payable to Lenders at Sofr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoanTrancheB5PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien incremental term loan tranche b-5 - payable to lenders at SOFR plus applicable margin.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoanTrancheB5PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Incremental Term Loan Tranche B-5 - Payable to Lenders at SOFR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net cash (used in) provided by financing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in financing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Liability Assumed, Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations and Disposal Groups [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ProviderServicesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Provider Services [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ProviderServicesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provider Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ProviderServicesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Provider services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortizationDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation and Amortization, Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortizationDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
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  <xsd:element id="btsg_NumberOfBranchesAcquired" name="NumberOfBranchesAcquired" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion" name="DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment" name="DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_TangibleEquityUnitsAmortizingNotesMember" name="TangibleEquityUnitsAmortizingNotesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ScheduleOfIntangibleAssetsTable" name="ScheduleOfIntangibleAssetsTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_MarchTwoThousandTwentySixOfferingMember" name="MarchTwoThousandTwentySixOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_TangibleEquityUnitsPurchaseContractsMember" name="TangibleEquityUnitsPurchaseContractsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_StockRepurchasedDuringPeriodShare" name="StockRepurchasedDuringPeriodShare" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_SummaryOfSignificantAccountingPolicyLineItems" name="SummaryOfSignificantAccountingPolicyLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_LongTermLiabilitiesTableTextBlock" name="LongTermLiabilitiesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderOperatingLeases" name="DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderOperatingLeases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_LcFacilityMember" name="LcFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockShare" name="ConversionOfTangibleEquityUnitsIntoCommonStockShare" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_InterestExpenseNetExpensesNotAllocatedAtSegmentLevel" name="InterestExpenseNetExpensesNotAllocatedAtSegmentLevel" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_SeniorAmortizingNoteMember" name="SeniorAmortizingNoteMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount" name="AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_EarningsPerShareLineItems" name="EarningsPerShareLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_GeneralAndProfessionalLiabilityInsuranceReservesLongTermLiabilitiesNoncurrent" name="GeneralAndProfessionalLiabilityInsuranceReservesLongTermLiabilitiesNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_PharmacySolutionsMember" name="PharmacySolutionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_SharesWithheldRelatedToNetShareSettlementShares" name="SharesWithheldRelatedToNetShareSettlementShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_AccruedLegalSettlementsAndProfessionalFeesCurrent" name="AccruedLegalSettlementsAndProfessionalFeesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases" name="DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DebtInstrumentFloorRate" name="DebtInstrumentFloorRate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_OtherAssetsGross" name="OtherAssetsGross" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_OtherDirectCosts" name="OtherDirectCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_SellingGeneralAndAdministrativeExpenseNotAllocatedAtSegmentLevel" name="SellingGeneralAndAdministrativeExpenseNotAllocatedAtSegmentLevel" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_ConsiderationForPurchaseOfRedeemableNoncontrollingInterestInAccountsPayable" name="ConsiderationForPurchaseOfRedeemableNoncontrollingInterestInAccountsPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_ExtinguishmentOfRedeemableNoncontrollingInterest" name="ExtinguishmentOfRedeemableNoncontrollingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_MedicareDMember" name="MedicareDMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_InterestRateSwapsNonCurrent" name="InterestRateSwapsNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_TaxEffectOfNetShareSettlementOfEquityAwardsValue" name="TaxEffectOfNetShareSettlementOfEquityAwardsValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DerecognitionOfRedeemableNoncontrollingInterestNetOfTax" name="DerecognitionOfRedeemableNoncontrollingInterestNetOfTax" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_ScottGreenwellMember" name="ScottGreenwellMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_DefiniteLivedLicensesMember" name="DefiniteLivedLicensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_TangibleEquityUnitsMember" name="TangibleEquityUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_SharesWithheldRelatedToNetShareSettlementValue" name="SharesWithheldRelatedToNetShareSettlementValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract" name="CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_NumberOfBranchesToBeAcquired" name="NumberOfBranchesToBeAcquired" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_SecondLienCreditAgreementMember" name="SecondLienCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_DerecognitionOfRedeemableNoncontrollingInterest" name="DerecognitionOfRedeemableNoncontrollingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_FinancingLeaseObligations" name="FinancingLeaseObligations" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_RelatedPartyTransactionsPolicyTextBlock" name="RelatedPartyTransactionsPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_DebtInstrumentDelayedDraw" name="DebtInstrumentDelayedDraw" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_FirstLienCreditAgreementMember" name="FirstLienCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_AccruedAutomobileInsuranceReservesCurrent" name="AccruedAutomobileInsuranceReservesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_LongTermLiabilitiesNoncurrent" name="LongTermLiabilitiesNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_SwinglineLoansMember" name="SwinglineLoansMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_NotionalAmountToHedgeCashFlowRiskOfVariability" name="NotionalAmountToHedgeCashFlowRiskOfVariability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockValue" name="ConversionOfTangibleEquityUnitsIntoCommonStockValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense" name="DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract" name="CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_SellingGeneralAndAdministrativeExpenseFromReportableSegment" name="SellingGeneralAndAdministrativeExpenseFromReportableSegment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_CommunityLivingBusinessMember" name="CommunityLivingBusinessMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_TwoThousandTwentySixAcquisitionMember" name="TwoThousandTwentySixAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear" name="PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_PaymentsForUnderwritingDiscountsAndCommissions" name="PaymentsForUnderwritingDiscountsAndCommissions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_TangibleEquityUnitsTextBlock" name="TangibleEquityUnitsTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_CertainPostClosingAdjustments" name="CertainPostClosingAdjustments" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_TrancheB6TermLoanMember" name="TrancheB6TermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_MedicareAMember" name="MedicareAMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_SummaryOfSignificantAccountingPolicyTable" name="SummaryOfSignificantAccountingPolicyTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_IssuanceOfDebtAndCommonStockPricePerShare" name="IssuanceOfDebtAndCommonStockPricePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet" name="GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_ForwardStartingContractsMember" name="ForwardStartingContractsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_JuneTwoThousandTwentySixOfferingMember" name="JuneTwoThousandTwentySixOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_TaxEffectOfNetShareSettlementOfEquityAwards" name="TaxEffectOfNetShareSettlementOfEquityAwards" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_CovenantsNotToCompleteMember" name="CovenantsNotToCompleteMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_DeferredIncomeTaxesExpenseBenefit" name="DeferredIncomeTaxesExpenseBenefit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_AmedisysAndLHCBranchesAcquisitionMember" name="AmedisysAndLHCBranchesAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_MorganStanleyMember" name="MorganStanleyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_NotesIssuedInConnectionWithAcquisitions" name="NotesIssuedInConnectionWithAcquisitions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_NotesReceivableNoncurrent" name="NotesReceivableNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_AlternateBaseRateMember" name="AlternateBaseRateMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_FirstLienIncrementalTermLoanTrancheB5PayableToLendersAtSofrPlusApplicableMarginMember" name="FirstLienIncrementalTermLoanTrancheB5PayableToLendersAtSofrPlusApplicableMarginMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_DirectCostsToSell" name="DirectCostsToSell" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1" name="BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations" name="CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_ScheduleOfIntangibleAssetsLineItems" name="ScheduleOfIntangibleAssetsLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_NotesPayableAndOtherMember" name="NotesPayableAndOtherMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember" name="RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_BusinessAcquisitionNumberOfBranches" name="BusinessAcquisitionNumberOfBranches" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_PrivateAndOtherMember" name="PrivateAndOtherMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderOperatingLeasesNetOfCurrentPortion" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderOperatingLeasesNetOfCurrentPortion" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_MedicaidMember" name="MedicaidMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CostOfDrugs" name="CostOfDrugs" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_AccruedChecksInExcessOfCashBalanceCurrent" name="AccruedChecksInExcessOfCashBalanceCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_AccruedPropertyInsuranceReserves" name="AccruedPropertyInsuranceReserves" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet" name="DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent" name="LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_CloudComputing" name="CloudComputing" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_DilutedEarningsLossPerShareAbstract" name="DilutedEarningsLossPerShareAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ProviderServicesMember" name="ProviderServicesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CreditAgricoleCorporateAndInvestmentBankMember" name="CreditAgricoleCorporateAndInvestmentBankMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_DoctorPayorNetworkMember" name="DoctorPayorNetworkMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_EarningsPerShareTable" name="EarningsPerShareTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CarryingAmountOfCommunityLivingBusiness" name="CarryingAmountOfCommunityLivingBusiness" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock" name="DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_EffectiveIncomeTaxRateReconciliationExpectedPercent" name="EffectiveIncomeTaxRateReconciliationExpectedPercent" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_ChangeInFairValueOfContingentConsiderationsNet" name="ChangeInFairValueOfContingentConsiderationsNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_DebtInstrumentConvertibleCashInstallmentPerUnit" name="DebtInstrumentConvertibleCashInstallmentPerUnit" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="btsg_IncomeTaxExpenseBenefitExpensesNotAllocatedAtSegmentLevel" name="IncomeTaxExpenseBenefitExpensesNotAllocatedAtSegmentLevel" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion" name="DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_RebateReceivableCurrent" name="RebateReceivableCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_FirstLienTermLoanMember" name="FirstLienTermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CreditAgricoleCorporateAndInvestmentBankOneMember" name="CreditAgricoleCorporateAndInvestmentBankOneMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_RepurchasesOfCommonStockInAccountsPayable" name="RepurchasesOfCommonStockInAccountsPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_CommonStockSharesPurchased" name="CommonStockSharesPurchased" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_FirstLienIncrementalTermLoanTrancheB6PayableToLendersAtSofrPlusApplicableMarginMember" name="FirstLienIncrementalTermLoanTrancheB6PayableToLendersAtSofrPlusApplicableMarginMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CommercialInsuranceMember" name="CommercialInsuranceMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_LcSublimitMember" name="LcSublimitMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_AmortizingNotesMember" name="AmortizingNotesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_StockRepurchasedDuringPeriodValues" name="StockRepurchasedDuringPeriodValues" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_NetLossExcludingAllocableRedeemableNoncontrollingInterests" name="NetLossExcludingAllocableRedeemableNoncontrollingInterests" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_ProfitLossExcludingRedeemableNoncontrollingInterests" name="ProfitLossExcludingRedeemableNoncontrollingInterests" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_IndefiniteLivedLicensesMember" name="IndefiniteLivedLicensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
