Less than I'd like, actually — the scene is connected with Missoula's, but it seems to be a somewhat loose connection (despite the two cities only being a three-hour drive through beautiful country from each other).

They do have a solid community, though, from everything I've heard so far. http://Startupbozeman.com has some info, and I went to the HATCH conference this year (http://hatchexperience.org/) which takes place in Bozeman, and met some wonderful representatives from the city. Good people, a nice downtown, and though not QUITE as walkable or cheap as Missoula, it's absolutely beautiful over there, and I always enjoy a visit.