There is a nice range about 20m west of Bozeman in Logan. It's membership based and costs $40/year and you have to have an NRA membership to join.http://www.manhattanwildlifeassociation.com/
There is an indoor range at the Gallatin County Fairgrounds that is open during the winter months. You can only shoot non-FMJ bullets that travel less than 1,400 fps.
There's a place up Hyalite canyon that a lot of people shoot at, but I don't like to shoot there. You can't shoot or see very far, so I've never felt that shooting there is very safe.
Other than that, you can shoot on pretty much any National Forest or BLM land. But the whole Gallatin County is pretty well populated, which means it's hard to find a spot to shoot anything besides pistol caliber and rimfire. If you're willing to drive 30-60 miles, wide open BLM land is not hard to find.
Bozeman is a college town, and as such, there are a fair amount of liberals here. But, most of them aren't your run of the mill liberals that you'll find in CA or NY. For example, my neighbor is a straight up granola. Home schools his kids, eats nothing but organic food, is concerned about the environment, etc. But he also raises chickens, goes hunting every year, and loves shooting my EBR's.