Crossing the border with a shotgun could be problematic.
I've lived on BC's north coast for 53 years. Big time hiking in my teens and twenties. Sea kayaked the whole coast after that. Been photographing in the bush for 40 years, mostly solo. Also worked in the bush at many different jobs, including living in a one room cabin all summer by myself counting fish for Fisheries, walking active spawning streams almost every day. Never carried a gun.
Have only had one close bear encounter, and it was my fault. Was a compassman with a guy putting in logging setting boundaries way back in the bush, but we didn't get along and were walking silently beside a mountain stream in spring. Heard a 'grunt' and looked up to see two black bear cubs climbing a tree. We did the same. Mom sat 1/2 between us and the cubs and calmly watched us. After a while we climbed down and sauntered out of there.
I also know a fellow who's been a traveling Fisheries guardian on BC's north coast for over 30 years who's job it is to count spawning salmon in rivers and streams. He carries two big cans of bear spray, one on each hip. No gun. He walks by himself and his wife stays on the boat.
My advice would be to carry bear spray, and make noise as you walk. My trick is to pick up a dry stick and whack tree trunks and rocks as I move through the bush. I got the idea after watching a documentary where the photographers got to know a bear so well, that it allowed them to follow it into the bush and sit beside it while the bear napped.
Even in a deep sleep, the bear would wake up instantly if it heard a small twig snapping in the bush. My theory is; snapping branches is what they're listening for, so if they hear me whacking tree trunks and rocks they must think to themselves, "
Hey, there's something BIG moving through the bush up ahead, and it doesn't care who hears it, so it must be a bad-ass".
So far (decades) so good
Another thought about guns...chances are you'll be charged in deep grass, thick salal, or huckleberry bushes where getting an accurate shot off is pretty much impossible.
Your odds will be much better avoiding them in the first place!