Bozeman doesn't have a lot of apartments available, so you want to start your hunt early. It is definitely not out of the question to start your search in the spring if you plan on moving in in the late summer. May is a great time to look for a place, as many of the students from the previous year will be on their way out of town.
You can use the small size of Bozeman to your advantage. If you happen to miss out on a place, don't be afraid to ask the landlord if he has any ideas for other places for rent. If you made a positive impression but just weren't the best candidate for that particular place, you may be able to get some great leads on other potential apartments this way.
The Streamline Bus System operates a free service that will get you a round to a few of the major points in Bozeman. Essentially, it does provide good connections between the University and Downtown, and along the south and east borders of the city. If you need to get a bit further afield on a regular basis, this is a city to own a car in.
Bozeman has a thriving cultural scene, and one of the best collections of museums for a city of its size in the country. The Museum of the Rockers, the Pioneer Museum and the Children's Museum are a just a few of the options. Sports fans throughout the city gather at Bobcat Stadium to support the University football team. If you're looking for a drink after the game, head to the intersection of 8th and main and take your pick of local watering holes.