If cleaning up tool marks, and rough spots in the bore is your intention, using either auto rubbing compound or JB Bore Paste is a hard way to go.
Professional bore lapping is done with silicon carbide or carborundum abrasive powder which even in the finest grade, is much, much more abrasive than the polishing compounds.
It won't hurt to try it anyway. When I was in military competitive shooting, we used to use Brasso brass polish for "breaking in" new barrels to make them smoother shooting.