I'll update this closer to the date since things change rapidly around here.
For one, consider a trip to Discovery Basin which is 120 miles from Bozeman. Its smaller than Bridger but really captures the small Montana resort atmosphere.
At Big Sky hit the tram during the week, the earlier in the week the better. If they get snow followed by sunshine hit Shedhorn chair early. It usually has great powder but the powder mushes out in the sun.
If you hit spring thaw/freeze conditions start on Thunder Wolf chair who's runs thaw first. As it melts head to Lone Mountain and work yourself up hill as the day goes by.
At Bridger take the mountain tour the resort hosts give.
Bridger is about 1/3 the size but you'll miss lots of it if you don't know your way around. If you have avalanche gear bring it so you can do the Ridge. Bribe a local with promises of beer or dinner so they'll show you the way, though.
I don't stay for dinner while at Big Sky so I don't have recommendations for restaurants. In Bozeman I like Spanish Peaks for Italian food, Montana Ale Works for microbrewery fare and The Garage for soup and Buffalo wings.