I live in Newfoundland, the province where the .303 British is simply known as "The Moose Gun" so that may give you some idea as to how particular we are when it comes to caliber selection.
Newfoundland has been blessed with some of the largest Black Bears on the planet. A combination of good genetics, zero predation and plentiful food sources accoding to our provincial wildlife biologists Shane Mahoney. As a result an "average" bear will run in the 350lb range, a "big" bear in the 450-550lb range and monsters in the 600-700-800lb range aren't that uncommon. Most black bears are taken as a secondary target of opportunity, as guys are moose and caribou hunting. They use whatever rifle they have with them at the time.
Getting back to my earlier statement, don't underestimate the .303 British! Its a great round and has accounted for hundreds of thousands of Moose and caribou in Newfoundland over the last 100 years. For Black Bears, however, I think that most any reasonable big game caliber will work fine. Put your rounds in the vitals and you get a dead bear. I've shot bears using the .303 Brit., .308 Win (my own handloads), 6.6X55mm Swede, .30-06, .30-30 & 7mm Rem Mag. I generally try for a shoulder shot to anchor the bear quickly. I haven't found them, even the really big bears, all that hard to kill, irrespective of the caliber used. Shot placement IMHO is far more important.
I usually take along a small block and tackle and 100' length of rope when I go hunting for animal recovery, especially when hunting alone. I've taken bear that I've had to quarter and pack out using my home made pack frame. I'm a big guy and can take a lot of weight, there are times when I had to hoist the pack frame using the block and tackle from a tree limb so I coule get it on my back! :shock: Don't know how heavy the bear was live weight, but those quarters were well over 100lbs a piece. That particular bear was taken with a plain ol' .308 Win. :grin: Most times, however, I try to either shoot my animal in a place where I can get my ATV (660 Yamaha Grizzly) to it, or can at least reach it with my 2500lb Warn Winch (rope comes in handy here too) :-)