I wouldn't use anything more aggressive than the JB Bore Paste, and I'd be a little careful with that.
Simply shooting the rifle will polish the bore.
There is no real advantage to having a bore that shines. Smooth yes, but not shinny.
Shooting will smooth the bore.
Using abrasives, even fine ones like JB can cause hundreds of rounds of wear on a new barrel, and can actually reduce it's life.
Having a bright, shiny bore is nice, but not at the expense of accuracy or service life.
