I assume you meant, Barkeepers Friend as I could find no reference to Bartenders Friend.
Barkeepers Friend contains feldspar powder which is an abrasive with a Mohs hardness of 7 on a scale of 1-10, 1 being talc and 10 being diamond. It also contains Oxalic acid which is a bleach.
I really don't think you want to use this on paint. Best to use a solvent, but one that doesn't dissolve the paint. Test first on an inconspicuous spot.