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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-03-05</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 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>0001409585</rptOwnerCik>
            <rptOwnerName>Coliseum Capital, 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>0001356974</rptOwnerCik>
            <rptOwnerName>COLISEUM CAPITAL PARTNERS L P</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>0001567187</rptOwnerCik>
            <rptOwnerName>Coliseum Capital Partners II, L.P.</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>0001454123</rptOwnerCik>
            <rptOwnerName>Gray Adam</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>0001635060</rptOwnerCik>
            <rptOwnerName>Coliseum School Bus Holdings, 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>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-03-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>61000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>9.03</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2561000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This transaction was executed in multiple trades at prices ranging from $8.98 to $9.05. The reported price reflects the weighted average purchase price. The Reporting Person filing this report hereby undertakes to provide upon request by the SEC staff, the Issuer or a shareholder of the Issuer full information regarding the number of shares purchased at each separate price.</footnote>
        <footnote id="F2">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, and (c) a separate account investment advisory client (the &quot;Separate Account&quot;) of CCM. Christopher Shackelton (&quot;Shackelton&quot;) and Adam Gray (&quot;Gray&quot;) are managers of CCM and CC. Following the transactions reported herein, CCP, CCP2 and the Separate Account directly owned 1,750,000, 310,000 and 501,000 shares of common stock, respectively.</footnote>
        <footnote id="F3">(Continued from footnote 2) Each of Shackelton, Gray, CCP, CCP2, the Separate Account, CC and CCM disclaim beneficial ownership of these securities except to the extent of that person's pecuniary interest therein.</footnote>
    </footnotes>

    <remarks>Adam Gray is a director of the Issuer. 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/ Christopher Shackelton, Manager</signatureName>
        <signatureDate>2015-03-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Christopher Shackelton</signatureName>
        <signatureDate>2015-03-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital, LLC, By: /s/ Christopher Shackelton, Manager</signatureName>
        <signatureDate>2015-03-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital Partners, L.P., By: Coliseum Capital, LLC, its General Partner, By: /s/ Christopher Shackelton, Manager</signatureName>
        <signatureDate>2015-03-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum Capital Partners II, L.P., By: Coliseum Capital, LLC, its General Partner, By: /s/ Christopher Shackelton, Manager</signatureName>
        <signatureDate>2015-03-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Adam Gray</signatureName>
        <signatureDate>2015-03-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Coliseum School Bus Holdings, LLC, By: Coliseum Capital Management, LLC, its Manager, By: /s/ Christopher Shackelton, Manager</signatureName>
        <signatureDate>2015-03-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
