To get to Big Sky, you need to fly into the Bozeman airport. It's rather small airport but sometimes that's a good thing. No confusion, the luggage came quick. We took a shuttle bus to Big Sky that took about 1 1/2 hours. We flew Alaska Airlines but there are many other airlines servicing the area. Since we intended on skiing, we brought our skies. We each had checked two pieces of luggage. First bag costs $15, second $25 (2010). Even the skis were considered just a second bag - no extra cost other than that.
Airport Code: BZN
850 Gallatin Field Road, Belgrade, MT 59714
This bus systems travels to key areas (not many) in Big Sky (including certain resort locations) and to Bozeman. It's free but they accept tips. Usually, on schedule and you can see the direction of travel as "Up Mountain" or "Down Mountain". We found it convenient when we went horse back riding and to the Hungry Moose market area.
Easiest way to get to the mountain village is to go with Karst Stage. They take you from the airport in Belgrade to the Hotel in a little more than 1 hour. Cost is about $80 for a return ticket.
I you stay in the mountain village it is no use to have a car.