I think it was something like 1000 strokes with JB that it took to smooth anything out. I've not tried that, but that's what a guy told me he did for all his rifles and it helped. So, take that with a grain of salt I guess.
The way I do it, and I actually just did this to a very nice barrel with a crappy throat reaming job, is to use 3m pads. The different color pads have different grit levels and you have to be careful. I'll take a maroon color 3m pad, a bronzer brush that is the next lower caliber (say a .284 brush for a .308 bore), cut a strip of the pad to fit on the whole brush perfectly when wrapping it around the brush, delaminate the pad into two pieces so that it's half as thick, then wrap the pad on the brush.
As you work the throat with the pad, it will break down and increase in fineness. After you're done, you use JBs to smooth the surface of that finish (or close the pores).
The detailed instructions can be found in Nathan Foster's guide to bolt action accurizing and maintenance. I wouldn't do it without reading this section in the book because you could screw it up. I've done it and it helps.