<?xml version="1.0" encoding="US-ASCII"?>
<!-- Generated by DFIN XBRL Schema Document - http://www.dfinsolutions.com/ - on 27-05-2026 07:18:06 AM -->
<!-- Copyright(c) 2026 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
<schema targetNamespace="http://www.blackrock.com/20260526" xmlns="http://www.w3.org/2001/XMLSchema" xmlns:bbfi="http://www.blackrock.com/20260526" xmlns:dei="http://xbrl.sec.gov/dei/2025" xmlns:srt-types="http://fasb.org/srt-types/2025" xmlns:deprecated="http://www.xbrl.org/2009/role/deprecated" xmlns:dtr="http://www.xbrl.org/2009/dtr" xmlns:oef="http://xbrl.sec.gov/oef/2025" xmlns:ref="http://www.xbrl.org/2006/ref" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xl="http://www.xbrl.org/2003/XLink" xmlns:us-gaap="http://fasb.org/us-gaap/2025" xmlns:oef-pre="http://xbrl.sec.gov/oef-pre/2025" xmlns:oef-lab="http://xbrl.sec.gov/oef-lab/2025" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:country="http://xbrl.sec.gov/country/2025" xmlns:us-roles="http://fasb.org/us-roles/2025" xmlns:enum2="http://xbrl.org/2020/extensible-enumerations-2.0" xmlns:us-types="http://fasb.org/us-types/2025" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2024-01-31" xmlns:oef-def="http://xbrl.sec.gov/oef-def/2025" xmlns:negated="http://www.xbrl.org/2009/role/negated" xmlns:xbrldi="http://xbrl.org/2006/xbrldi" xmlns:srt="http://fasb.org/srt/2025" xmlns:oef-sr="http://xbrl.sec.gov/oef-sr/2025" xmlns:srt-roles="http://fasb.org/srt-roles/2025" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:stpr="http://xbrl.sec.gov/stpr/2025" elementFormDefault="qualified">
	<import namespace="http://www.xbrl.org/2003/instance" schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd"/>
	<import namespace="http://www.xbrl.org/2003/linkbase" schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd"/>
	<import namespace="http://xbrl.sec.gov/dei/2025" schemaLocation="https://xbrl.sec.gov/dei/2025/dei-2025.xsd"/>
	<import namespace="http://fasb.org/us-types/2025" schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-types-2025.xsd"/>
	<import namespace="http://www.xbrl.org/dtr/type/2024-01-31" schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd"/>   
	<import namespace="http://xbrl.sec.gov/country/2025" schemaLocation="https://xbrl.sec.gov/country/2025/country-2025.xsd"/>
	<import namespace="http://fasb.org/srt/2025" schemaLocation="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd"/>
	<import namespace="http://fasb.org/srt-types/2025" schemaLocation="https://xbrl.fasb.org/srt/2025/elts/srt-types-2025.xsd"/>
	<import namespace="http://xbrl.sec.gov/oef-sr/2025" schemaLocation="https://xbrl.sec.gov/oef/2025/oef-sr-2025.xsd"/>
	<import namespace="http://fasb.org/us-gaap/2025" schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd"/>
	<import namespace="http://fasb.org/us-roles/2025" schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-roles-2025.xsd"/>
	<import namespace="http://fasb.org/srt-roles/2025" schemaLocation="https://xbrl.fasb.org/srt/2025/elts/srt-roles-2025.xsd"/>
	<annotation>
		<appinfo>
			<link:linkbase id="lnk">
				<link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/domain-member" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#domain-member"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/ShareholderReport" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#ShareholderReport"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/ShareholderReportHoldingsDetails" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#ShareholderReportHoldingsDetails"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/ShareholderReportLineGraphDetails" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#ShareholderReportLineGraphDetails"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/ShareholderReportAverageAnnualReturnDetails" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#ShareholderReportAverageAnnualReturnDetails"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/ClassOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#ClassOnly"/>
				<link:roleRef roleURI="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists" xlink:type="simple" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-roles-2025.xsd#eedm"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/LargestHoldingOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#LargestHoldingOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/Other1CategoryOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#Other1CategoryOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/AdditionalIndexOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#AdditionalIndexOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/BroadBasedIndexOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#BroadBasedIndexOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/Other2CategoryOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#Other2CategoryOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/SalesLoadOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#SalesLoadOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/MaturityOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#MaturityOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/IndustrySectorOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#IndustrySectorOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/CreditQualityOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#CreditQualityOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/GeographicRegionOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#GeographicRegionOnly"/>
				<link:presentationLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/ShareholderReport">              
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_ShareClassDomain" xlink:label="ShareClassDomain"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011391Member" xlink:label="C000011391Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011391Member" order="2.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052631Member" xlink:label="C000052631Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000052631Member" order="3.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037620Member" xlink:label="C000037620Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000037620Member" order="4.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037618Member" xlink:label="C000037618Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000037618Member" order="5.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011387Member" xlink:label="C000011387Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011387Member" order="6.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052630Member" xlink:label="C000052630Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000052630Member" order="7.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011390Member" xlink:label="C000011390Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011390Member" order="8.0" />
				</link:presentationLink>
				<link:presentationLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/ShareholderReportHoldingsDetails">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_ShareClassDomain" xlink:label="ShareClassDomain"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011391Member" xlink:label="C000011391Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011391Member" order="2.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052631Member" xlink:label="C000052631Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000052631Member" order="3.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037620Member" xlink:label="C000037620Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000037620Member" order="4.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037618Member" xlink:label="C000037618Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000037618Member" order="5.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011387Member" xlink:label="C000011387Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011387Member" order="6.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052630Member" xlink:label="C000052630Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000052630Member" order="7.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011390Member" xlink:label="C000011390Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011390Member" order="8.0" />   
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember" xlink:label="InvestmentTypeCategorizationMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_ForeignAgencyObligationsMember" xlink:label="ForeignAgencyObligationsMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="ForeignAgencyObligationsMember" order="2.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_FixedRateLoanInterestsMember" xlink:label="FixedRateLoanInterestsMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="FixedRateLoanInterestsMember" order="3.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_PreferredSecuritiesMember" xlink:label="PreferredSecuritiesMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="PreferredSecuritiesMember" order="4.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_InvestmentCompaniesMember" xlink:label="InvestmentCompaniesMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="InvestmentCompaniesMember" order="5.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_FloatingRateLoanInterestsMember" xlink:label="FloatingRateLoanInterestsMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="FloatingRateLoanInterestsMember" order="6.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_ForeignGovernmentObligationsMember" xlink:label="ForeignGovernmentObligationsMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="ForeignGovernmentObligationsMember" order="7.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_USTreasuryObligationsMember" xlink:label="USTreasuryObligationsMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="USTreasuryObligationsMember" order="8.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_NonAgencyMortgageBackedSecuritiesMember" xlink:label="NonAgencyMortgageBackedSecuritiesMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="NonAgencyMortgageBackedSecuritiesMember" order="9.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_USGovernmentSponsoredAgencySecuritiesMember" xlink:label="USGovernmentSponsoredAgencySecuritiesMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="USGovernmentSponsoredAgencySecuritiesMember" order="10.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetBackedSecuritiesMember" xlink:label="AssetBackedSecuritiesMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="AssetBackedSecuritiesMember" order="11.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WarrantMember" xlink:label="WarrantMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="WarrantMember" order="12.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember" xlink:label="CommonStockMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="CommonStockMember" order="13.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MunicipalBondsMember" xlink:label="MunicipalBondsMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="MunicipalBondsMember" order="14.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateBondSecuritiesMember" xlink:label="CorporateBondSecuritiesMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="InvestmentTypeCategorizationMember" xlink:to="CorporateBondSecuritiesMember" order="15.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_MaturityDomain" xlink:label="MaturityDomain"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_OtherCategory1Domain" xlink:label="OtherCategory1Domain"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_OtherCategory2Domain" xlink:label="OtherCategory2Domain"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_LargestHoldingsDomain" xlink:label="LargestHoldingsDomain"/>
					<!--GeographicRegionDomain Only presentation and label linkbases-->			 
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_GeographicRegionDomain" xlink:label="GeographicRegionDomain"/>
					<!--IndustrySectorDomain Only presentation and label linkbases-->	
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_IndustrySectorDomain" xlink:label="IndustrySectorDomain"/>	
					<!--CreditQualityDomain Only presentation and label linkbases-->	
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_CreditQualityDomain" xlink:label="CreditQualityDomain"/>	
					<link:loc xlink:type="locator" xlink:href="#bbfi_NRMember" xlink:label="NRMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="CreditQualityDomain" xlink:to="NRMember" order="2.0" />
					<!--ExternalCreditRatingFitchMember Only presentation and label linkbases-->	
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ExternalCreditRatingFitchMember" xlink:label="ExternalCreditRatingFitchMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="CreditQualityDomain" xlink:to="ExternalCreditRatingFitchMember" xbrldt:usable="false" order="1.0"/>
					<!--ExternalCreditRatingMoodysMember Only presentation and label linkbases-->	
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ExternalCreditRatingMoodysMember" xlink:label="ExternalCreditRatingMoodysMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="CreditQualityDomain" xlink:to="ExternalCreditRatingMoodysMember" xbrldt:usable="false" order="2.1"/>
					<!--ExternalCreditRatingStandardPoorsMember Only presentation and label linkbases-->	
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ExternalCreditRatingStandardPoorsMember" xlink:label="ExternalCreditRatingStandardPoorsMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="CreditQualityDomain" xlink:to="ExternalCreditRatingStandardPoorsMember" xbrldt:usable="false" order="3.1"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsCCRatingMember" xlink:label="StandardPoorsCCRatingMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ExternalCreditRatingStandardPoorsMember" xlink:to="StandardPoorsCCRatingMember" order="1.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsCCCRatingMember" xlink:label="StandardPoorsCCCRatingMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ExternalCreditRatingStandardPoorsMember" xlink:to="StandardPoorsCCCRatingMember" order="2.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsBRatingMember" xlink:label="StandardPoorsBRatingMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ExternalCreditRatingStandardPoorsMember" xlink:to="StandardPoorsBRatingMember" order="3.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsBBRatingMember" xlink:label="StandardPoorsBBRatingMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ExternalCreditRatingStandardPoorsMember" xlink:to="StandardPoorsBBRatingMember" order="4.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsBBBRatingMember" xlink:label="StandardPoorsBBBRatingMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ExternalCreditRatingStandardPoorsMember" xlink:to="StandardPoorsBBBRatingMember" order="5.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsARatingMember" xlink:label="StandardPoorsARatingMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ExternalCreditRatingStandardPoorsMember" xlink:to="StandardPoorsARatingMember" order="6.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsAARatingMember" xlink:label="StandardPoorsAARatingMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ExternalCreditRatingStandardPoorsMember" xlink:to="StandardPoorsAARatingMember" order="7.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsAAARatingMember" xlink:label="StandardPoorsAAARatingMember"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ExternalCreditRatingStandardPoorsMember" xlink:to="StandardPoorsAAARatingMember" order="8.0" />
					<!--CreditRatingAMBestDomain Only presentation and label linkbases-->	
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CreditRatingAMBestDomain" xlink:label="CreditRatingAMBestDomain"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="CreditQualityDomain" xlink:to="CreditRatingAMBestDomain" xbrldt:usable="false" order="4.1"/>
				</link:presentationLink>
				<link:presentationLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/ShareholderReportLineGraphDetails">            
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_ShareClassDomain" xlink:label="ShareClassDomain"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011391Member" xlink:label="C000011391Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011391Member" order="2.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052631Member" xlink:label="C000052631Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000052631Member" order="3.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037620Member" xlink:label="C000037620Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000037620Member" order="4.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037618Member" xlink:label="C000037618Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000037618Member" order="5.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011387Member" xlink:label="C000011387Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011387Member" order="6.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052630Member" xlink:label="C000052630Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000052630Member" order="7.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011390Member" xlink:label="C000011390Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011390Member" order="8.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_AdditionalIndexDomain" xlink:label="AdditionalIndexDomain"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_BroadBasedIndexDomain" xlink:label="BroadBasedIndexDomain"/>
				</link:presentationLink>
				<link:presentationLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/ShareholderReportAverageAnnualReturnDetails">            
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_ShareClassDomain" xlink:label="ShareClassDomain"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011391Member" xlink:label="C000011391Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011391Member" order="2.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052631Member" xlink:label="C000052631Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000052631Member" order="3.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037620Member" xlink:label="C000037620Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000037620Member" order="4.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037618Member" xlink:label="C000037618Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000037618Member" order="5.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011387Member" xlink:label="C000011387Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011387Member" order="6.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052630Member" xlink:label="C000052630Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000052630Member" order="7.0" />
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011390Member" xlink:label="C000011390Member"/>
					<link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ShareClassDomain" xlink:to="C000011390Member" order="8.0" />
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_AdditionalIndexDomain" xlink:label="AdditionalIndexDomain"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_BroadBasedIndexDomain" xlink:label="BroadBasedIndexDomain"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_WithSalesLoadMember" xlink:label="WithSalesLoadMember"/>
				</link:presentationLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/ClassOnly">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_ShareClassDomain" xlink:label="ShareClassDomain"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011391Member" xlink:label="C000011391Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000011391Member" order="1.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052631Member" xlink:label="C000052631Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000052631Member" order="2.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037620Member" xlink:label="C000037620Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000037620Member" order="3.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037618Member" xlink:label="C000037618Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000037618Member" order="4.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011387Member" xlink:label="C000011387Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000011387Member" order="5.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052630Member" xlink:label="C000052630Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000052630Member" order="6.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011390Member" xlink:label="C000011390Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000011390Member" order="7.0"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/Other1CategoryOnly">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_OtherCategory1Domain" xlink:label="OtherCategory1Domain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/Other2CategoryOnly">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_OtherCategory2Domain" xlink:label="OtherCategory2Domain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/LargestHoldingOnly">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_LargestHoldingsDomain" xlink:label="LargestHoldingsDomain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/SalesLoadOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_WithSalesLoadMember" xlink:label="WithSalesLoadMember"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember" xlink:label="InvestmentTypeCategorizationMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_ForeignAgencyObligationsMember" xlink:label="ForeignAgencyObligationsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="ForeignAgencyObligationsMember" order="1.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_FixedRateLoanInterestsMember" xlink:label="FixedRateLoanInterestsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="FixedRateLoanInterestsMember" order="2.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_PreferredSecuritiesMember" xlink:label="PreferredSecuritiesMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="PreferredSecuritiesMember" order="3.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_InvestmentCompaniesMember" xlink:label="InvestmentCompaniesMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="InvestmentCompaniesMember" order="4.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_FloatingRateLoanInterestsMember" xlink:label="FloatingRateLoanInterestsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="FloatingRateLoanInterestsMember" order="5.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_ForeignGovernmentObligationsMember" xlink:label="ForeignGovernmentObligationsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="ForeignGovernmentObligationsMember" order="6.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_USTreasuryObligationsMember" xlink:label="USTreasuryObligationsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="USTreasuryObligationsMember" order="7.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_NonAgencyMortgageBackedSecuritiesMember" xlink:label="NonAgencyMortgageBackedSecuritiesMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="NonAgencyMortgageBackedSecuritiesMember" order="8.0"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_USGovernmentSponsoredAgencySecuritiesMember" xlink:label="USGovernmentSponsoredAgencySecuritiesMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="USGovernmentSponsoredAgencySecuritiesMember" order="9.0"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MunicipalBondsMember" xlink:label="MunicipalBondsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="MunicipalBondsMember" order="10.0"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/BroadBasedIndexOnly">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_BroadBasedIndexDomain" xlink:label="BroadBasedIndexDomain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/AdditionalIndexOnly">              
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_AdditionalIndexDomain" xlink:label="AdditionalIndexDomain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/MaturityOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_MaturityDomain" xlink:label="MaturityDomain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/IndustrySectorOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_IndustrySectorDomain" xlink:label="IndustrySectorDomain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/CreditQualityOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_CreditQualityDomain" xlink:label="CreditQualityDomain"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_NRMember" xlink:label="NRMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="CreditQualityDomain" xlink:to="NRMember" order="1.0"/>
				</link:definitionLink>
				<!--GeographicRegionOnly use only for STPR-->
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/GeographicRegionOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_GeographicRegionDomain" xlink:label="GeographicRegionDomain"/>
				</link:definitionLink>
				<link:labelLink xlink:type="extended" xlink:role="http://www.xbrl.org/2003/role/link">               
					<link:loc xlink:type="locator" xlink:href="#bbfi_NRMember" xlink:label="NRMember"/>
					<link:label xlink:type="resource" xlink:label="label_NRMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">N R [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="NRMember" xlink:to="label_NRMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_ForeignAgencyObligationsMember" xlink:label="ForeignAgencyObligationsMember"/>
					<link:label xlink:type="resource" xlink:label="label_ForeignAgencyObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Foreign Agency Obligations [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ForeignAgencyObligationsMember" xlink:to="label_ForeignAgencyObligationsMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_FixedRateLoanInterestsMember" xlink:label="FixedRateLoanInterestsMember"/>
					<link:label xlink:type="resource" xlink:label="label_FixedRateLoanInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Fixed Rate Loan Interests [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="FixedRateLoanInterestsMember" xlink:to="label_FixedRateLoanInterestsMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_PreferredSecuritiesMember" xlink:label="PreferredSecuritiesMember"/>
					<link:label xlink:type="resource" xlink:label="label_PreferredSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Preferred Securities [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="PreferredSecuritiesMember" xlink:to="label_PreferredSecuritiesMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_InvestmentCompaniesMember" xlink:label="InvestmentCompaniesMember"/>
					<link:label xlink:type="resource" xlink:label="label_InvestmentCompaniesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Investment Companies [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="InvestmentCompaniesMember" xlink:to="label_InvestmentCompaniesMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_FloatingRateLoanInterestsMember" xlink:label="FloatingRateLoanInterestsMember"/>
					<link:label xlink:type="resource" xlink:label="label_FloatingRateLoanInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Floating Rate Loan Interests [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="FloatingRateLoanInterestsMember" xlink:to="label_FloatingRateLoanInterestsMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_ForeignGovernmentObligationsMember" xlink:label="ForeignGovernmentObligationsMember"/>
					<link:label xlink:type="resource" xlink:label="label_ForeignGovernmentObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Foreign Government Obligations [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ForeignGovernmentObligationsMember" xlink:to="label_ForeignGovernmentObligationsMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_USTreasuryObligationsMember" xlink:label="USTreasuryObligationsMember"/>
					<link:label xlink:type="resource" xlink:label="label_USTreasuryObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">U S Treasury Obligations [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="USTreasuryObligationsMember" xlink:to="label_USTreasuryObligationsMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_NonAgencyMortgageBackedSecuritiesMember" xlink:label="NonAgencyMortgageBackedSecuritiesMember"/>
					<link:label xlink:type="resource" xlink:label="label_NonAgencyMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Non Agency Mortgage Backed Securities [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="NonAgencyMortgageBackedSecuritiesMember" xlink:to="label_NonAgencyMortgageBackedSecuritiesMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_USGovernmentSponsoredAgencySecuritiesMember" xlink:label="USGovernmentSponsoredAgencySecuritiesMember"/>
					<link:label xlink:type="resource" xlink:label="label_USGovernmentSponsoredAgencySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">U S Government Sponsored Agency Securities [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="USGovernmentSponsoredAgencySecuritiesMember" xlink:to="label_USGovernmentSponsoredAgencySecuritiesMember"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011391Member" xlink:label="C000011391Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000011391Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000011391 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000011391Member" xlink:to="label_C000011391Member"/>
										<link:label xlink:type="resource" xlink:label="label_C000011391Member_2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xml:lang="en-US">Class R</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000011391Member" xlink:to="label_C000011391Member_2"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052631Member" xlink:label="C000052631Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000052631Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000052631 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000052631Member" xlink:to="label_C000052631Member"/>
										<link:label xlink:type="resource" xlink:label="label_C000052631Member_2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xml:lang="en-US">Class K</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000052631Member" xlink:to="label_C000052631Member_2"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037620Member" xlink:label="C000037620Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000037620Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000037620 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000037620Member" xlink:to="label_C000037620Member"/>
										<link:label xlink:type="resource" xlink:label="label_C000037620Member_2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xml:lang="en-US">Investor C</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000037620Member" xlink:to="label_C000037620Member_2"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000037618Member" xlink:label="C000037618Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000037618Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000037618 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000037618Member" xlink:to="label_C000037618Member"/>
										<link:label xlink:type="resource" xlink:label="label_C000037618Member_2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xml:lang="en-US">Investor A1</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000037618Member" xlink:to="label_C000037618Member_2"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011387Member" xlink:label="C000011387Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000011387Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000011387 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000011387Member" xlink:to="label_C000011387Member"/>
										<link:label xlink:type="resource" xlink:label="label_C000011387Member_2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xml:lang="en-US">Investor A</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000011387Member" xlink:to="label_C000011387Member_2"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000052630Member" xlink:label="C000052630Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000052630Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000052630 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000052630Member" xlink:to="label_C000052630Member"/>
										<link:label xlink:type="resource" xlink:label="label_C000052630Member_2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xml:lang="en-US">Service</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000052630Member" xlink:to="label_C000052630Member_2"/>
					<link:loc xlink:type="locator" xlink:href="#bbfi_C000011390Member" xlink:label="C000011390Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000011390Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000011390 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000011390Member" xlink:to="label_C000011390Member"/>
										<link:label xlink:type="resource" xlink:label="label_C000011390Member_2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xml:lang="en-US">Institutional</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000011390Member" xlink:to="label_C000011390Member_2"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetBackedSecuritiesMember" xlink:label="AssetBackedSecuritiesMember"/>
					<link:label xlink:type="resource" xlink:label="label_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Asset-Backed Securities [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="AssetBackedSecuritiesMember" xlink:to="label_AssetBackedSecuritiesMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WarrantMember" xlink:label="WarrantMember"/>
					<link:label xlink:type="resource" xlink:label="label_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Warrant [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="WarrantMember" xlink:to="label_WarrantMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember" xlink:label="CommonStockMember"/>
					<link:label xlink:type="resource" xlink:label="label_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Common Stock [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="CommonStockMember" xlink:to="label_CommonStockMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MunicipalBondsMember" xlink:label="MunicipalBondsMember"/>
					<link:label xlink:type="resource" xlink:label="label_MunicipalBondsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Municipal Bonds [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="MunicipalBondsMember" xlink:to="label_MunicipalBondsMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateBondSecuritiesMember" xlink:label="CorporateBondSecuritiesMember"/>
					<link:label xlink:type="resource" xlink:label="label_CorporateBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Corporate Bond Securities [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="CorporateBondSecuritiesMember" xlink:to="label_CorporateBondSecuritiesMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsCCRatingMember" xlink:label="StandardPoorsCCRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsCCRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, CC Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsCCRatingMember" xlink:to="label_StandardPoorsCCRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsCCCRatingMember" xlink:label="StandardPoorsCCCRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsCCCRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, CCC Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsCCCRatingMember" xlink:to="label_StandardPoorsCCCRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsBRatingMember" xlink:label="StandardPoorsBRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsBRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, B Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsBRatingMember" xlink:to="label_StandardPoorsBRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsBBRatingMember" xlink:label="StandardPoorsBBRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsBBRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, BB Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsBBRatingMember" xlink:to="label_StandardPoorsBBRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsBBBRatingMember" xlink:label="StandardPoorsBBBRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsBBBRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, BBB Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsBBBRatingMember" xlink:to="label_StandardPoorsBBBRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsARatingMember" xlink:label="StandardPoorsARatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsARatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, A Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsARatingMember" xlink:to="label_StandardPoorsARatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsAARatingMember" xlink:label="StandardPoorsAARatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsAARatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, AA Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsAARatingMember" xlink:to="label_StandardPoorsAARatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsAAARatingMember" xlink:label="StandardPoorsAAARatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsAAARatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, AAA Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsAAARatingMember" xlink:to="label_StandardPoorsAAARatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis" xlink:label="InvestmentTypeAxis"/>
					<link:label xlink:type="resource" xlink:label="label_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Investment Type [Axis]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="InvestmentTypeAxis" xlink:to="label_InvestmentTypeAxis" priority="1"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="AssetsNet"/>
					<link:label xlink:type="resource" xlink:label="label_AssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Net Assets</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="AssetsNet" xlink:to="label_AssetsNet" priority="1"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyPortfolioTurnover" xlink:label="InvestmentCompanyPortfolioTurnover"/>
					<link:label xlink:type="resource" xlink:label="label_InvestmentCompanyPortfolioTurnover" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Investment Company Portfolio Turnover</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="InvestmentCompanyPortfolioTurnover" xlink:to="label_InvestmentCompanyPortfolioTurnover" priority="1"/>                
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_NoTradingSymbolFlag" xlink:label="dei_NoTradingSymbolFlag"/>
					<link:label xlink:type="resource" xlink:label="label_NoTradingSymbolFlag" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">No Trading Symbol Flag</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_NoTradingSymbolFlag" xlink:to="label_NoTradingSymbolFlag" priority="1"/>		
				</link:labelLink>
			</link:linkbase>
		</appinfo>
	</annotation>   
	<element name="NRMember" id="bbfi_NRMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="ForeignAgencyObligationsMember" id="bbfi_ForeignAgencyObligationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="FixedRateLoanInterestsMember" id="bbfi_FixedRateLoanInterestsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="PreferredSecuritiesMember" id="bbfi_PreferredSecuritiesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="InvestmentCompaniesMember" id="bbfi_InvestmentCompaniesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="FloatingRateLoanInterestsMember" id="bbfi_FloatingRateLoanInterestsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="ForeignGovernmentObligationsMember" id="bbfi_ForeignGovernmentObligationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="USTreasuryObligationsMember" id="bbfi_USTreasuryObligationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="NonAgencyMortgageBackedSecuritiesMember" id="bbfi_NonAgencyMortgageBackedSecuritiesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="USGovernmentSponsoredAgencySecuritiesMember" id="bbfi_USGovernmentSponsoredAgencySecuritiesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000011391Member" id="bbfi_C000011391Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000052631Member" id="bbfi_C000052631Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000037620Member" id="bbfi_C000037620Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000037618Member" id="bbfi_C000037618Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000011387Member" id="bbfi_C000011387Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000052630Member" id="bbfi_C000052630Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000011390Member" id="bbfi_C000011390Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
</schema>
