When I lived in AK, I most often carried a Taurus Raging Bull .454 Casull loaded with 360 hard cast Buffalo Bore ammo during hunting, fishing, hiking expeditions. When walking the dog around the 'burbs of Anchorage, most often a 4" S&W 629 .44 mag. with 305 grain hard cast Buffalo Bore ammo. The best gun shop in Alaska, Great Northern Guns, stocked Buffalo Bore ammo. There are other options available. But, to me, the key is a heavy for bore diameter semi-wadcutter, or wide flat nosed bullet, to better one's odds of minimizing deflection and obtaining deep penetration.
"Wyosmith" gives solid advice in his post above. If a bear decides to maul you, you will be lucky to get a couple of shots off "while you are vertical".