Why not ship your own bike there using Bikeflights or Shipbikes? You could almost certainly ship round trip for less than $200.
As noted above, it's not the best road cycling the state has to offer, but there is some decent riding. If you will have a car and some time I can offer you some suggestions. I have done a fair amount of touring to the west of Bozeman, passing through places like Ennis, Twin Bridges and Butte. The climb from Whitehall up to Pipestone Pass on MT 2 is fun. The climb from Ennis towards Virginia City will put hair on your chest and offers a great view of Madison Valley. About a 2 hr. drive away is a place called Wise River, which sits at the northern end of the Pioneer Mountains Scenic Byway. You can climb to one degree or another for 26 miles. Very scenic. Closer to the summit is a stunning alpine meadow. The Byway is part of the Great Divide Mountain Bike Route. It's paved now, but wasn't until 2008.