I live just outside of the Eastern Rockies in Alberta and do a lot of climbing/scrambling in the mountains. I've run into grizzlies on a few occasions (always when I've been alone) but, surprisingly, never any black bears. The first time, I was way out in the back-country and had just sprained my ankle jumping across a stream. I followed the trail to where it descended a short, steep embankment and there was a momma grizzly and her cub less than 10m below me digging up roots or grubs. Fortunately, when I surprised her she grunted and moved backwards instead of coming at me. Unfortunately, she was right on the trail and I couldn't go around her because of cliffs. I walked back down the trail towards her, making tons of noise, and she and the cub slowly moseyed on up the trail, taking their sweet time, until they eventually headed off into the bush and I could safely get past. It was a pretty awesome but unsettling experience. I've also seen grizzlies a few times at a safer distance.
Bears are like people, in that they all have their own personalities. You just have to hope that you don't run into a grumpy one, who's having a bad day. Having said that, you're far more likely to die on the highway on your way to the mountains, than you are to die to a bear in the wilderness. Annual deaths to grizzly bears for all of North America averages something like 1 or 2 a year. In most attacks, they're just defending their cubs or their turf. Predatory attacks are extremely rare.