Downtown Bozeman is compact and walkable. A car is needed for the surrounding outdoor areas — Bridger Bowl, Hyalite Canyon, and Yellowstone all require driving. Parking downtown is generally available and free in many areas.
Streamline is the city bus system, serving routes through the city including the university. It is free to ride. For the ski area and canyon day trips, car rental or a local shuttle service is the practical option.
Cycling is viable in good weather; the city has a growing network of bike paths. The trail along Sourdough Creek connects downtown to the university and is a pleasant route.