paparock,
your choice of a heavy hard cast bullet is a good one. they will penetrate much better than a standard 240 gr 44 soft point.
as velodog (a long time alaskan) noted above, a handgun is a practical weapon to carry and have on you when doing all the normal activities here in the alaska bush. i have seen fisherman carry shotguns, and very occasionally a rifle. those weapons always (not mostly, ALWAYS) get set down to allow freedom of movement when casting a rod, setting up camp, taking a crap, etc. if you need a gun, the bear might be between you and the gun or closer to it than you are.
a 44 mag (i carry a 45 long colt with 330's) in a GUIDES CHOICE shoulder holster is the best way to carry a large handgun and make sure you have a weapon on you when you absolutely need it at any moment. it actually saved the life of a bear hunter up here a couple springs ago, the son shot the bear off his father (who was terribly mauled) because he had a 454 casull in a guides choice holster on him when the bear attacked.
if i was hunting a bear, i would use a large caliber rifle, but ANY gun is better than a sharp stick in a bear encounter. a handgun is just an insurance policy. you never want to use it, but god have mercy on you if you don't have one and need it.
full disclosure, i have pulled my handgun a couple of times, but never actually needed to use it during any bear encounters. i CAN tell you though, my non gun packing buddies were glad that somebody was armed when we had a young 8 ft brown bear hassling us over some sock eye salmon. thankfully, he left the river to us after walking in on us a couple of times. or last year when a black bear ran into our camp to see what was available to eat. my granddaughters darted off like a covey of quail. i pulled the pistol, but did not need to shoot anybody.

but if needed, I COULD HAVE.