I don't know if it's the 'best' way, but for me the easiest and quickest way for a round bbl (if you don't have a lathe) is to use some wet-dry emery on top of a sponge. Grab one end of the bbl, wet the emery and run it back and forth until the pitting is removed. Repeat with finer cloth to whatever finish you like. Generally speaking, anything over 400 grit is counterproductive if you want to end up with a satin finish; the blueing process will tone the finish down more than 400 will leave on the surface.
If you want the 'grain' to remain parallel to the length, stop after the 'back and forth' polishing. If you want it to show as going around the diameter like a lathe-turned finish, twist the bbl while applying the abrasive, doing one section at a time until the entire length is done.
Draw-filing is fine for octagonal bbls, not for round. Using a polishing wheel is fine if you have some experience, but the surface can end up wavy and uneven if you're not careful.