<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4/A</documentType><periodOfReport>2003-03-31</periodOfReport><dateOfOriginalSubmission>2003-03-31</dateOfOriginalSubmission><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000013610</issuerCik><issuerName>BOWNE &amp; CO INC</issuerName>        <issuerTradingSymbol>BNE</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001179913</rptOwnerCik><rptOwnerName>SCHWARZ H MARSHALL</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>BOWNE &amp; CO., INC.,</rptOwnerStreet1><rptOwnerStreet2>345 HUDSON STREET</rptOwnerStreet2><rptOwnerCity>NEW YORK</rptOwnerCity><rptOwnerState>NY</rptOwnerState><rptOwnerZipCode>10014</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>Options to Purchase Common Stock</value></securityTitle><conversionOrExercisePrice><value>9.4983</value></conversionOrExercisePrice><transactionDate><value>2003-03-31</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>7012</value><footnoteId id="F1" /></transactionShares><transactionPricePerShare><value>0</value><footnoteId id="F2" /></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2004-12-31</value></exerciseDate><expirationDate><value>2013-12-31</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>7012</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>7012</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Non-qualified stock options granted under The Stock Plan for Directors first adopted in 1997. This amendment properly reflects the allocation of securities or derivative securities, as the case may be, to this Reporting Person in respect of quarterly compensation for Board Service.</footnote><footnote id="F2">Non-qualified stock options granted under The Stock Plan for Directors first adopted in 1997.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ H. Marshall Schwarz</signatureName><signatureDate>2003-08-04</signatureDate></ownerSignature></ownershipDocument>

