Ed,
I've taken both a 454 Ruger SRH and a .338-06JDJ to Alaska several times and didn't have any problems. Your .358 would be my choice. Although, in 4 trips up there, I've yet to see any bears. I have had one of my caribou ate on, had griz in camp dragging off meat and have seen alot of bear sign, but have not laid eyes on one except from a bush plane. So you might think about packing a side arm of some sort, but for bou and blackies either would work.
Good luck this fall. This will be the first time in 4 straight years I will not be going up
, so I'll be root'in for ya! Let us know how you do.
Rugernut