I killed the bear in my avatar with a Marlin 1894 in .44 mag caliber. I was still hunting in the mountains here in TN down an old closed forest service road and happened to spot the bear coming up the mtn before it saw me. The bear passed about 25 yds in front of me walking and I put a 240 gr Winchester white box round that I bought at Wally World behind it's shoulder. I had a complete pass thru and the bear ran about 20 to 25 yds up hill after the shot. Huge blood trail and the bear was not moving at all when I got to it. Now some more info, the bear was not a large one, about 150 lbs tops. It was walking like I said, not alerted at all to my presence and finally, the shot was close and behind the shoulder. Not many animals survive a shot to the heart/lung area. We can't hunt over bait in TN but at the distances you hunt over bait the .44 should work. I would however keep in mind the possibility of how large a bear you could possibly kill and take that in consideration when choosing a caliber. We do have 300 to 400# bears and some were taken, mostly with a handgun because TN allows the use of dogs to hunt/tree the bear which most hunters here do (obviously not me). The hunter then has time (usually) to pick his shot. Also a hand gun is a lot easier to carry in the thick woods when you don't know where a bear will tree.
I will hunt again this year but with a 30-30 and 170 grn bullets and I don't feel undergunned but that is just my opinion. Anyway, good luck, Lonnie.