There are a number of options for bus transportation in and around the Canadian Rockies:
To get to the mountains, the best bet is Brewster Bus Lines, the pioneer in mountain transport (it's owned by Gray Lines, the tour bus people). Their buses leave from downtown Calgary, or if you are arriving with a chrter flight, from the airport. Laidlaw tranpsortation also has regular bus service to the Rockies. There are also several smaller shuttle buses that will take you from Calgary International. Check at the airport for schedules and pricing.
To get to and from the airport in Calgary, use the Cardinal "Airporter" with its buses painted like red cardinals.
Their buses travel every half hour between downtown
Calgary hotels and the airport (for $12, its a lot cheaper than a cab).
If you are not heading to a downtown hotel, then the Airport Shuttle Express is a good bet, at $16 a person.
To get to Banff from Calgary airport by bus, there are two competing services. The Banff Airporter (403-2762-3330 or toll-free 1-800-661-1152) with 8 shuttles a day, and Sky Link (toll-free at 1-888-642-5252) with 6 shuttles a day. The cost runs about $44 each way to Banff $52 to Lake Louise ($22 and $25, respectively, for children up to 15 years). Both requre redervations for the return trip from Banff or Canmore to the airport.
Greyhound is the major in-out bus company in Canada (1 800 661 8747). You go from the Canadian Rockies to practically everywhere in North America with them. Greyhound has several departures a day eastbound (towards Winnipeg & Toronto) and westbound (towards Vancouver).
If you need to get around Alberta, the Red Arrow will take you to Red Deer, Edmonton, Rocky Mountain House, and Fort McMurray. Their luxury coaches have comfortable seating, free pop, cookies, magazines, and videos with several departures a day from Calgary.
You can also charter a bus. This is great if you travel in a group (a company ski trip, for example). This makes sure that, if you're drinking, nobody is driving, and that everybody gets to your destination together.
By the way, if your're looking for the CHEAPEST way to get into Calgary from the airport (all you backpackers and students), catch the the Calgary Transit bus from the airport to the Northeast LRT. The bus leaves every half hour throughout the day (not into the evenings), and lets you transfer for the LRT (light rail transit) into downtown for an investment of $2.00. The train ends at 10th Street SW, where you can catch a Greyhound shuttle to catch a Groundhound bus to wherever you're heading. The shuttle is free and comes every half hour. (If you need to trasfer to the Anderson/South LRT, get off at City Hall/Olympic Plaza, and to transer to the Brentwood/Northwest LRT get off & transfer at the 8 Street SW station).
NOTE for 2012: the West leg of the LRT is a continuation of the Northeast Leg, will have a Sunalta stop beside the Greyhound station.
Find Local Bus Companies (charter & scheduled).