<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-09-29</periodOfReport>

    <issuer>
        <issuerCik>0002097545</issuerCik>
        <issuerName>AMG BBH Asset-Backed Credit Fund, LLC</issuerName>
        <issuerTradingSymbol>BBASX</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0002073844</rptOwnerCik>
            <rptOwnerName>AMG New York Holdings Corp.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>600 HALE STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PRIDES CROSSING</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01965</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>false</isDirector>
            <isOfficer>false</isOfficer>
            <isTenPercentOwner>true</isTenPercentOwner>
            <isOther>false</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>false</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class S units of beneficial interest</value>
            </securityTitle>
            <transactionDate>
                <value>2026-09-29</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>false</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>280701.754</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.40</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1822463.816</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <ownerSignature>
        <signatureName>/s/ Kavita Padiyar, President and Secretary</signatureName>
        <signatureDate>2026-10-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
