4Bear are huge here in coastal NC. Bear hunting is a family tradition for over 8 generations. If a flintlock and ball will drop a bear, a 30-06 should have no problem. I've used my 10mm on 2. Solid black shot at 15 yards. Pass through. DRT. Light cinnamon 27 yards in ground blind with a 12 gauge next to me. It was walking and a behind the ear shot DRT.
.243 on a small 190lb bear. Reload with Speer hot-core 100gr bullet. It went 30ish yards before giving up life.
All others have been with my 06 and a 165gr Speer Hot Core or a Grand Slam loaded at my bench. If I was going to have too use factory ammo, it would be Winchester power max bonded 180gr. You could take a broad side or slightly quartering shot from 1 foot too 400 yards. That load is GREAT on large hogs as well.
I hope your hunt was good and hope future hunts are even better.
P.S. almost all bear carry trichanosis. Cook too a minimum of 145°.