I'n not sure what seasoning the bore really means... everyone it seems has a different slant on it nowadays, but to smooth out any rough edges in the bore, shooting is a great remedy.. though I don't know that I'd waste any round balls on it. I'd waste whatever I was gonna be hunting with.
You might want to take your range rod and wrap some steel wool over the jag and just run through your barrel 50 or 100 times, making sure that as much as possible, try to get the whole bore evenly. You could finish up with some really fine steel wool or some rouge on a patch.
You're gonna love black powder hunting if your guns shoot straight, and this is why practice on the range and trying different bullets will go a long way to building your confidence.
aloha...