Gee, you are at the doorway of the park!
You can take MT84 West, US191 South to W.Yellowstone. Another route is to take I-90E followed by US89 South to Gardiner. So you can do a loop:
MT84-US191-W.Yellowstone-Madison-Old Faithful-Lake-Canyon-Tower Falls-Mammoth-US89-I90-Back to Bozeman.