I love Big Sky, There is a ton of terrain. But I think it might be a bit isolated for 2 weeks.
Of course, you could do 5 days in Yellowstone National Park staying at the Snow lodge with the rest at Big Sky. That'd be a tremendous adventure.
The West Yellowstone entrance is about 45 miles from Big Sky. You'd want to stay at the Snow Lodge at Old Faithful. You will need to arrange transport from West Yellowstone to Old Faithful yourself -- Xanterra, the park concessionaire, no longer operates a snow coach from West Yellowstione. There are several tour companies that will take you from West Yellowstone to Old Faithful -- it's not cheap, but it is a snow coach and an adventure!
It will take half a day to get from West Yellowstone to the Snow Lodge (and vice versa). There are several tours that the concessionaire organizes. We did the photography tour (full day) and the Canyon snowshoe (also a full day). Both were excellent and you get to see many animals, thermal features, and incredible scenery in the park. Yellowstone is a treasure and absolutely spectacular in winter, not the least of why is because no one is there. Old Faithful is one of the premier nordic skiing areas in North America. You can ski from the lodge. They rent skis and snowshoes. They also provide incredibly inexpensive and high quality nordic ski instruction.
You can get direct air service from a number of US gateways to Bozeman. Here's the page with info for last ski season.http://bigskyresort.com/plan-a-trip/how-to-get-here/airlines-and-direct-flights
You'd probably want to rent a car for the duration you are here. You can usually get a pretty inexpensive rental for a week (or more) at Bozemen. A car will allow you to drive to Big Sky (45 miles from Bozeman), to West Yellowstone, to Buck's T-8 restaurant for dinner (highly recommended) and into Bozeman to visit Bridger for a bit more variety in skiing.
Also, you should definitely hire Ursula Howland of the Big Sky Ski School as a guide/instructor. She'll get you the goods, sort the terrain for you, give some excellent instruction, and be a fine friend.