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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-05-16</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001589526</issuerCik>
        <issuerName>Blue Bird Corp</issuerName>
        <issuerTradingSymbol>BLBD</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001409751</rptOwnerCik>
            <rptOwnerName>Coliseum Capital Management, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001430708</rptOwnerCik>
            <rptOwnerName>Shackelton Christopher S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001409585</rptOwnerCik>
            <rptOwnerName>Coliseum Capital, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001356974</rptOwnerCik>
            <rptOwnerName>COLISEUM CAPITAL PARTNERS, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001567187</rptOwnerCik>
            <rptOwnerName>Coliseum Capital Partners II, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001454123</rptOwnerCik>
            <rptOwnerName>Gray Adam</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001635060</rptOwnerCik>
            <rptOwnerName>Coliseum School Bus Holdings, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>105 ROWAYTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROWAYTON</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06853</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-05-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>128369</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.80</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>994246</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">These securities are held directly by (a) Coliseum Capital Partners, L.P. (&quot;CCP&quot;), an investment limited partnership of which Coliseum Capital, LLC, a Delaware limited liability company (&quot;CC&quot;), is general partner and for which Coliseum Capital Management, LLC, a Delaware limited liability company (&quot;CCM&quot;), serves as investment adviser, (b) Coliseum Capital Partners II, L.P. (&quot;CCP2&quot; and, together with CCP, the &quot;Funds&quot;), an investment limited partnership of which CC is general partner and for which CCM serves as investment adviser, (c) Coliseum School Bus Holdings, LLC (&quot;CSB&quot;) and (d) a separate account investment advisory client of CCM (the &quot;Separate Account&quot;).</footnote>
        <footnote id="F2">Christopher Shackelton (&quot;Shackelton&quot;) and Adam Gray (&quot;Gray&quot;) are managers of CCM and CC. CSB is a company through which CCP, CCP2 and Separate Account have invested in the Issuer's 7.625% Series A Convertible Cumulative Preferred Stock. CCM is the manager of CSB. Each of Shackelton, Gray, CCP, CCP2, the Separate Account, CC, CSB and CCM disclaim beneficial ownership of these securities except to the extent of that person's pecuniary interest therein.</footnote>
        <footnote id="F3">Following the transactions reported herein, CCP, CCP2, the Separate Account and CSB directly owned 783,243; 62,166; 148,837; and 0 shares of common stock, respectively.</footnote>
    </footnotes>

    <remarks>Adam Gray is a director of the Blue Bird Corporation (the &quot;Issuer&quot;). As a result, the following persons may be deemed directors by deputization of the Issuer solely for purposes of Section 16 of the Securities Exchange Act of 1934, as amended: Coliseum Capital Management, LLC; Coliseum Capital, LLC; Coliseum Capital Partners, L.P.; Coliseum Capital Partners II, L.P.; Coliseum School Bus Holdings, LLC and Christopher Shackelton.</remarks>

    <ownerSignature>
        <signatureName>Coliseum Capital Management, LLC, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-05-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Christopher Shackelton, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-05-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital, LLC, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-05-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital Partners, L.P., By: /s/  Thomas Sparta, Attorney-in-fact, By: Coliseum Capital, LLC, its General Partner, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-05-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital Partners II, L.P., By: Coliseum Capital, LLC, its General Partner, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-05-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Adam Gray, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-05-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum School Bus Holdings, LLC, By: Coliseum Capital Management, LLC, its Manager, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-05-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
