An excellent bore polishing paste that works as well as JB’s can be made from equal parts of BonAmi™, paste wax (like Johnson & Johnson or Butchers), and light oil. The BonAmi is the “doesn’t scratch” product. Regular abrasive cleansers may be too harsh for use in a bore.
Another old standby is to use a hand type automobile rubbing compound and a larger than normal sized bore brush (say, one size larger–.25 in a .22 bore, .33 in a .30, etc.).
For both of these methods you will need a rod that allows the tip to rotate as it passes through the bore.
To use either of these solutions strip the action and clamp horizontally in padded vise jaws. Clean the barrel normally. Then, run the rod through the bore from the breach end, attach the oversized brush and coat with the compound. The pull it back through the bore to the chamber (don’t allow it to clear the chamber, to help keep “stuff” out of the action) and repeat this 25 or 30 times. Then with the brush outside the muzzle remove the brush and then pull the rod out of the barrel. Then attach a proper sized jag and a clean patch to the rod and from the breach work the patch back and forth several times. Repeat this with clean patches until the patch comes out clean.
Thoroughly flush the chamber and action with solvent to remove any grit, and then reclean the bore and chamber with normal bore cleaner. Your bore will be noticeable cleaner and smoother.
I recently tested some MAAS Metal Polishing Creme made by MAAS International. While not designed as a bore paste it did a very nice job on smoothing out several barrels and left them very clean and shiny. First clean the barrel normally with both regular bore cleaner and a copper remover. Then coat a patch with the MAAS and using a tight fitting jag work it through the bore using a series of short strokes. Repeat several times with a new patch and polish and then final clean with bore cleaner to remove any residue. It is not as aggressive as JB or the above homemade stuff so it may not work as well on a really rough bore. The MAAS Polishing Creme is available at some Walmart, Home Depots, Walgreens, ACE, Tru-Serv, others in a 2 ounce size for about $4 and on line at www.maasinc.com in a 4 ounce size for about $12.