Like the man (Hawgstoppah) said in a post from way back in this thread "Be aware, make noise, carry bear spray and fish with a friend if possible".
Having a second home a 10 minute walk from the Crow, I've fished it, the Castle all the way up to its origins, the Oldman, the Waterton, Belly and St. Mary's over the last 25 years. Both walking/wading and preferably (if my good bud makes it down from Edmonton) two vehicles and a loaded Metzler for multi-day float trips.
So I'll add some humble thoughts about fishing down here:
1. pay attention to the wind intensity and direction (down, up, cross). Yes, there have been dead-calm days down here (on the hottest ones, no less) so a bear/cougar has a chance to hear you coming. Otherwise, pay attention to the wind and blind corners and watch the shadows. More often than not, there's a beastie in one of them. Make noise. Especially if wandering off for a bio-break. PS: if you want cougar country straight out of the movies, the lower Oldman is the place to be.
2. switch sides. I've encountered bears early in the season (hungry) and late (hungry). Not so much in the middle, although hardly a fast rule, that. Late in the season, almost always on the sunny side, hunting berries in the windfree pockets (yes, there are lots of berries around here, mostly the Crow). So switch banks and carry on. Obviously after giving the bear his due and time to wander off.
3. fish alone with a buddy. Huh? If you're lucky to have a bud to do this with, make sure (especially if floating) to stop at a likely pool or lip-smackin' spot and have one of you (the guy who caught the last fish, for instance) "spot" the other, by climbing up an embankment or high spot to watch for any locals that may arrive announced. Can't tell you how many times that's paid off.
4. bears are very territorial. If you arrive first at a berry spot, they'll let you have it. Of course, you don't have a firm way of judging if you're first, but fresh berries with no signs of trampling might be one way. That said, any signs of bear such as that very trampling, carcasses (calf or cow), and/or fresh scrub piles (probably hiding fresh kill) are a sure sign to beat it out, and fast.
Avalanche danger or warnings stop me dead. Bears and cougars don't. Within reason. Get out there and enjoy, safely - it's great country down here.