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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-09-27</periodOfReport>

    <notSubjectToSection16>1</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Former Director</otherText>
        </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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Former Director</otherText>
        </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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Former Director</otherText>
        </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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Former Director</otherText>
        </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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Former Director</otherText>
        </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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Former Director</otherText>
        </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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Former Director</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-09-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2907</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2907</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-09-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2907</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>19.65</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Equivalent Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-09-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2907</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2907</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Restricted Stock Equivalent Units convert into Common Stock on a one-for-one basis.</footnote>
        <footnote id="F2">For each vested Restricted Stock Equivalent Unit (&quot;RSEU&quot;), Blue Bird Corporation (the &quot;Issuer&quot;) will make a cash payment to Coliseum Capital Partners, L.P. (&quot;CCP&quot;) equal to the fair market value of a share of the Issuer's common stock on the Settlement Date. &quot;Settlement Date&quot; means the earlier of (i) the date Adam Gray's (&quot;Gray&quot;) continuous service on the board of the Issuer terminates for any reason or (ii) the date of the consummation of a change of control. The RSEUs vest on April 2, 2018. On September 27, 2017, Mr. Gray ended his service on the board of the Issuer. Therefore, the fair market value of the shares of RSEU were
equal to the closing price of the Issuer's Common Stock on September 27, 2017.</footnote>
        <footnote id="F3">The RSEUs were held by CCP pursuant to an agreement under which Gray assigned to CCP the right to receive all compensation (including equity compensation) that Gray would otherwise receive as a director of the Issuer.</footnote>
        <footnote id="F4">These securities were held directly by CCP, 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. Coliseum Capital Partners II, L.P. (&quot;CCP2&quot; and, together with CCP, the &quot;Funds&quot;) is an investment limited partnership of which CC is general partner and for which CCM serves as investment adviser.</footnote>
        <footnote id="F5">Christopher Shackelton (&quot;Shackelton&quot;) and Gray are managers of CCM and CC. Coliseum School Bus Holdings, LLC (&quot;CSB&quot;) is a Delaware limited liability company through which CCP, CCP2 and a separate account investment advisory client of CCM (the &quot;Separate Account&quot;) 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>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Coliseum Capital Management, LLC, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-28</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Christopher Shackelton, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-28</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital, LLC, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-28</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital Partners, L.P.
By: Coliseum Capital, LLC, its General Partner, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-28</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>2017-09-28</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Adam Gray, By: /s/  Thomas Sparta, Attorney-in-fact</signatureName>
        <signatureDate>2017-09-28</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>2017-09-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
