<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-09-30</periodOfReport><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>15.015</value></conversionOrExercisePrice><transactionDate><value>2003-09-30</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>4436</value><footnoteId id="F1" /></transactionShares><transactionPricePerShare><value>0</value><footnoteId id="F1" /></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>4436</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>4436</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.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ H. Marshall Schwarz</signatureName><signatureDate>2003-09-30</signatureDate></ownerSignature></ownershipDocument>

