I am from the UP of Michigan where bears, cougars and blood sucking mosquitoes are always a concern when hiking, hunting or fishing.
In my humble opinion, I would be less concerned with the type of ammunition and more concerned with the amount of accurate shots I could deliver to an upset Bear. I am assuming, that we are talking about a revolver here. I would really suggest a semi-automatic 40 S&W or 45 with a couple of xtra clips and a pair high end running shoes.
Just remember, if you run out of ammo and the bear is still grumpy: You don't have to outrun the bear, just the person your hiking with.