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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-03-20</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>METRO CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>1 STATION PLACE, 7TH FLOOR SOUTH</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06902</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001430708</rptOwnerCik>
            <rptOwnerName>Shackelton Christopher S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>METRO CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>1 STATION PLACE, 7TH FLOOR,</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06902</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001409585</rptOwnerCik>
            <rptOwnerName>Coliseum Capital, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>METRO CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>1 STATION PLACE, 7TH FLOOR,</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06902</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001356974</rptOwnerCik>
            <rptOwnerName>COLISEUM CAPITAL PARTNERS, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>METRO CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>1 STATION PLACE, 7TH FLOOR,</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06902</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001567187</rptOwnerCik>
            <rptOwnerName>Coliseum Capital Partners II, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>METRO CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>1 STATION PLACE, 7TH FLOOR,</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06902</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001454123</rptOwnerCik>
            <rptOwnerName>Gray Adam</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>METRO CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>1 STATION PLACE, 7TH FLOOR,</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06902</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001635060</rptOwnerCik>
            <rptOwnerName>Coliseum School Bus Holdings, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>METRO CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>1 STATION PLACE, 7TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06902</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-03-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>464570</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1172615</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-03-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>50000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1122615</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 862,754; 82,435; 177,426; 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/  Chivonne Cassar, Attorney-in-fact</signatureName>
        <signatureDate>2017-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Christopher Shackelton, By: /s/  Chivonne Cassar, Attorney-in-fact</signatureName>
        <signatureDate>2017-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital, LLC,  By: /s/  Chivonne Cassar, Attorney-in-fact</signatureName>
        <signatureDate>2017-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital Partners, L.P., By: Coliseum Capital, LLC, its General Partner,  By: /s/  Chivonne Cassar, Attorney-in-fact</signatureName>
        <signatureDate>2017-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital Partners II, L.P.,  By: Coliseum Capital, LLC, its General Partner,  By: /s/  Chivonne Cassar, Attorney-in-fact</signatureName>
        <signatureDate>2017-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Adam Gray,  By: /s/  Chivonne Cassar, Attorney-in-fact</signatureName>
        <signatureDate>2017-03-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum School Bus Holdings, LLC, By: Coliseum Capital Management, LLC, its Manager,  By: /s/  Chivonne Cassar, Attorney-in-fact</signatureName>
        <signatureDate>2017-03-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
