The thing about a bear is they can bounce up and down a lot when charging you. Just aim for the mouth as best you can - you want to his the brain stem because that's they only place that really stops any animal dead in it's tracks other than snapping the spine but the spine isn't even seen on a charging bear.
You're only hope, really, is dumb luck and the biggest, most powerful, hardcast cartridge you can fire at it. I'd say that once a brown bear decides to charge at you things start to look really bleak really quick. You have a chance with a black bear but a costal brown or even a grizzly is about the most dangerous critter on dry land. You'll be lucky to get off one round and not likely at all to get off two unless you start shooting when they're 50 yards away. And unfortunately our govt. has decided that you have to wait to see if it's a bluff charge before you start shooting. IMO jail is better than the cemetary though. YMMV.
The caveat with my comments is that I have zero actual experience shooting a charging bear of any kind, like most people. I only know what I read or see on tv.