One point: an AR-15 is not really adequate for bear. It's probably not adequate to large deer, it's more of a "varmint" gun, though you can use it for antelope. For deer and black bears, you need a .30 caliber, either a .308 Winchester (which is basically the 7.62 NATO used in, e.g., the FN FAL battle rifle) or a .30-06.
For grizzlies, even .30 caliber isn't adequate, they take a "big game" rifle. I suppose one of those .50 BAR anti-materiel rifles could do in a pinch, though.