90% of the bear attacks the bear is on you before you can say "What the ____"
I've camped hunted and hiked in almost every state in the union, and seen 2 bears in the wild, both were running away.
If you are determined to have a gun, buy a Remington 870 rifled slug gun "that's a 12 gauge shot gun with a rifled barrel". they are light to carry. very accurate and will stop most any bear, if you have time to get it off your shoulder.
I feel your concern is a little over the top. the national park service will know of any bear active in the area(park) and will close the trails. heed the signs and forget the gun.