First I clean the barrel as best I can.
I use a copper solvent & Kroil or Marvel Mystery oil.
Then I wrap patch around worn brush with JB on it.
I will swab 100 strokes with brush & JB.
Then I will shoot 1 round and Clean.
I do this for 5 rounds.
Then shoot 5 rounds and clean,Till the barrel settles in, you will be able to tell when copper is not showing too quickly.
I clean with JB each time.
JB will not be needed everytime once the barrel polishes up, but I won`t hesitate to use it if needed.
Barrel will usually come into it`s own pretty quickly.
I recently did this with an old Mossberg 140 K and it`s shooting in the .4`s @50yds. So you can sometimes save an old gun this way too.
Now I won`t say this is the Right way, it`s just my way.