Thank you for the info.The Teton Pass over the mountains is pretty steep (3671ft up and 5213ft down) but people do it all the time. 88.6 miles, 1hr 47 mins on Google (for a car). Depends on your confidence. Link below will show you the route as if you were cycling it as it shows elevation change.
You can take the longer route which is not too bad 191, 89, 26 but will be a longer drive. 109 miles, 2 hours10 minutes on Google (for a car). This is mostly flat, again see link for cycling elevation info.