I have used a 270, 45-70, 338 and 9.3x64brenneke they all worked well.
The biggest "trick" is identifying the vitals. A bear can just look like a black blob making it hard to see where to hit. On any kind of reasonable angle away from me, I look for the far leg use that to estimate where the bottom of the far shoulder is and drive one in there trying to take out near side lungs and far leg/shoulder. If the bear is angled towards I do the opposite punching through the near shoulder/leg and out the far lung.
This shot has always worked well and will drop them very close to, if not, right on the spot.