I have spen a lot of time bicycle touring and hiking in the ranges from Waterton/Glacier National Park northwest to Jasper Alberta. Bikes give you great views of the water. As an angler I am always thinking about which streams that I have seen to which would like to return in the future. While my list is not extensive, I would recommend that you do some further reading about these waters...Crowsnest River near Pincher Creek (town name), Elk River in Sparwood, Fernie, etc, and what I think is the High River from Peter Laugheed Provincial Park just SE of Banff downstream to Longview. I saw local kids fly fishing the Elk and reviewed some literature that mentioned a range of coldwater species. Crowsnest River was being fished at a few locations every time I went through there and I had heard that it was good. That was one that was hard not to fish...what a beauty. And High River just looked fishy, but if I recall correctly, it was a bull trout River so there may be restrictions. As I said, do research on these just as I would plan to do, if I was thinking about fishing out there.
As for the Bow River, it is famous in the Calgary area, but you won't find mountains in Calgary. Farther upstream it is in the mountains, but no research I did when there suggested that it was great fishing in the mountains, plus it was always off color from glacier melt. Likewise for the beautiful Kootenay River in Kootenay National Park. It is a beautiful spot, but the glacial wash is substantial. Heard that the Kootenay can be good downstream in MT, however. Just some thoughts about where you could begin your research and what you may want the avoid.