One year ago this month, my neighbor shot a Black Bear, using a 240gr jacketed soft point, with his Ruger .44 Redhawk. Shot the bear center of the shoulder at 15 yards, from a tree stand. There is a bank behind the tree stand, putting the bear at the same level as we were. Thought sure we had a dead bear. Bear squalled and rolled around for a minute then beelined out of there for about 100 yards. We could hear and see it, throwing a fit for the next 30 minutes of so. Then the bear disappeared, before I could get a good shot at it with my rifle. About two hours later the bear was shot by the fellows in our other tree stand half a mile away. Bear was coming in for bait. The bullet from the pistol had punched a hole in the shoulder blade, broke a rib, then deflected up and lodged above the lungs, and below the spine. This shot would not have killed this bear.
Then again last month a man in Anchorage shot and killed a Grizzly while hiking on a bike path. This man shot the bear with a Ruger .44 mag. Did not say what bullet he was using. Personally I would use the heaviest bullet I could shoot accurately, any time I went after bear.