It's easy to let small dangers occupy larger portions of our minds than they should.
My first time in grizzly country was back in 2003. I did a summer internship with the fisheries department in Yellowstone. Bears were fairly commonly encountered.
We did an eight day backpacking trip on the Upper Yellowstone to catch and tag Yellowstone Cutthroats. It was a joint project with Wyoming Game and Fish as we actually got out of the park to the south. There were two of us from NPS, two from WGF, and a volunteer (a doctor from Livingston, as I recall) who provided some horses.
This was during the Cutthroat spawn, before the season opened. The whole area was closed to the public because of bear activity.
We spent a couple nights in ranger cabins and the rest in tents. One night while while we were in a cabin a bear got the horses very uneasy. They were inside a battery powered electric fence which was being used to keep the bears out, not the horses in. That was the only confirmed presence of a bear on the trip until we were working our way back down the river to be picked up by a boat on the lake.
Three of us, the NPS biologist, a WGF tech, and myself were walking the river looking for a few more fish while the WGF biologist and volunteer were using a trail to move the horses. I think my boss had a sixth sense for bears as he got very cautious all of the sudden and started scanning the area. We came into a small clearing in the willows and he shouted something that I didn't understand but, when I turned, there was a grizzly coming straight at us. We all pulled our bear spray but, fortunately, the bear ended its bluff charge before we had to discharge. It was close, really close.
I'd be lying if I said it didn't shake me up. I've been able to keep it in perspective, though. I know I'm still far more likely to die in a car driving to an area with bears than I am to be killed by a bear. My wife is a teacher and she gets worked up over active shooter drills. While scary and tragic, her students are at far more risk while driving to school, not to mention all the other risky behaviors teenagers participate in.
Be cautious and alert. If you find or smell a carcass, keep moving. Absolutely take precautions but the presence of bears won't keep me from enjoying the places they inhabit. I don't go searching for stories of deadly or harmful bear encounters but it seems many involve a bear defending a kill site. The animal may have be killed by wolves or a hunter. It doesn't matter who or what killed it, once the bear has claimed it, it's his.
Stay away from carcasses, make noise, and carry bear spray and appreciating the beautiful places that bears live doesn't have to be done from a distance.
The fact that bears don't kill dozens of moronic tourists in Yellowstone each year is solid proof that they're not out to get us.
One thing regarding a shotgun, I don't know how well you'd make out taking one to Canada for self defense purposes. Also, bear spray on your hip is more accessible than a slung shotgun and a lot easier to fish with. In the unlikely event that you'll need it, very quick access matters. That bear can be on top of you in no time.