A lot of folks swear by the 10mm's for wilderness duty. Fact is, I think that if you can manage to hit the bear between the eyes as it is charging you I think that the 45GAP will do the trick but I am not a ballistics expert.
I wouldn't go for the head, the skull might just ricochet off the rounds and piss him off. (This is what a hunter told me a long time ago so that might be wrong). Go for the heart or maybe take out a limb.
I wouldn't want to face a large grizzly with anything less than a hot 10mm or .44 Mag, but the .45GAP will do everything the .45ACP will do...I'd be unloading on the thing though. My .45GAP is my preferred carry round. I think, if I were in an area where I was at risk of running into a bear when walking the dog, that I would probably look for something a little more potent for dog walking duty.
Lots of variables...like the size of the bear and how close you are and what type rounds are you carrying...In simple terms, it is not the BEST round for the job, but a well placed round to the heart would work..especially the scrawny brown bears here in Kalifornia...I would be more concerned if it was a Kodiak or a Grizzly in which case a .44 magnum would be my first choice for handgun, or better yet, a .308 rifle at 300 yards, lol. Still, multiple, well placed rounds with a .45 should work.