A good, cheap hotel in Banff is the Voyager Inn, and they run shuttles
to the hill. Another cheap one is Bumper's Inn. There's also a hostel,
but you're on your own for transpo.

There's tons of shuttle companies, just google calgary banff shuttle or
something like that. They're not exactly cheap as I recall, $50+ one
way. They go from Calgary to Banff but not directly to the hills.

Neil