Hi,
I do the same as handirifle does except that i clean all jb's out of bore between new patches of jb.
I then shot my new polished gun with various kinds of cheap factory ammo (100 rounds total). Groups opened up to 2-3 inches after initially shooting 1.25 inches at 100 yards. SO, i did the jb process again and cleaned the barrel really well afterwards. I then broke in the barrel by shooting one round at a time, a light cleaning between rounds, for 20 rounds. Afterwards, i lightly cleaned the barrel and began shooting 5 shot strings. ALL groups, with el cheapo ammo, were under 1.25 inches, with sub MOA's coming from Winchester fodder.
I am not sure if the break in did anything. it is likely the second round of polishing and cleaning did the trick. HOWEVER, it never hurts to break in a barrel either...