There are a couple of options. The most convenient way is to rent a 4WD car, this allows you maximum flexibility, but it comes at a cost because you 100% need 4WD. Next most convenient option would be to hire a private shuttle, expect each way in an SUV to cost around $300. Potentially less expensive would be share a shuttle. Ride Share (Uber/ Lyft) are rumored to do this run, but it is recommended to go through an actual shuttle company as they employ professional drivers in vehicles equipped to handle the potentially precarious roads. There are currently 14-shuttle companies offering this service, haven’t heard anything bad about any yet. There is no bus service from BZN to Big Sky.