I have made the drive to Big Sky to Anaconda and back in one day.
From Big Sky to Bozeman, the road is good but is two lane. Once you get out of Bozeman, it is pedal to the metal on the interstate. At 170 miles, however, 2 hours seems your fastest possibility. I would think you would be able to make it in 2-1/2 hours easily. I would not plan a lot less than that.