Don't expect to see a lot of bears, unless you want to and know where they are. After thousands of days in the Alberta wilderness I have had only a few face-to-face bear encounters on hiking trails. If you want to see bears go to Waterton. Although there are bears in Banff park they are rarely seen. I've seen black bears in Jasper park, usually from the road. It would be typical that you would spend your entire holiday and not see a bear. Don't be disappointed. I've had only one face to face encounter with (two) grizzly bears on the trail, over a lifetime living in Alberta. Never anything violent, but I do carry bear spray, which you could buy when you arrive (you're not supposed to carry aerosol sprays on a plane). Don't time your holiday based on bear activity, as from a human perspective there is little difference.
The best photo time to visit may be the early fall, as the Larch (tamarak) trees are dropping their orange needles. Weather wise, if you are tenting, you want to come in August or early September. The latter is dramatically less crowded as the kids are back in school. Anything before May is cold, and many mountain passes cannot be hiked until after late July because of snow pack. September is cold, but from a photo-op perspective you will have light snow dusting mountains and changing colors in the trees.