I will say that PA bear hunting is a bit different than some black bear hunting in some places.
1. We have big bears at times - over 800# seems to happen every year. Not the norm, but they are out there.
2. Most of our bear are shot in the thick laurel mountainous terrain of the state. Usually a flash of black at "short" range is all you get to decide on.
3. Most of our hunting is done in drives which has a tendency to create running shots on alert, determined running bears.
4. We have a HIGH population of hunters - not unusual if you miss or don't knock it down now, the next guy will in a few minutes.
All that said, of the maybe two dozen or so bears I've been on drives that we killed, almost all were killed with factory cup and core lead bullets, few died on the spot, and two holes in 'em (or more if you can) is never a bad thing. Esp. in laurel! I recall a 400# one with a 280 Rem (head shot standing) - bang, flop of course, two 500#'s - two 30-30's and a 7mm Mag respectively - chest shots - all were running and continued to for a bit with multiple kill shots in them, and one 600# with 7mm Mag - standing or walking as I recall - bang, flop pretty much - chest shot broadside - no exit. I'll never tell you to not go bigger cal or heavier or better bullets for bear, but most deer cal's will do it - they're not made of kevlar, but can be determined and tend not to let too much blood out and no hoof print (LOL!) if you do need to track them. Many are killed each year with 30-30's and 243's. Both of your cal's are plenty. Get a good accurate load with a heavier, premium bullet, and you can't do much better. JMHO.