I'm quite familiar with that route. It's very scenic. The one thing, though, is that a very good portion of it is winding. You see a LOT of white crosses on that stretch of U.S. 191. I tried counting one time and it was almost 40, with a shocking number of multiple fatalities. The portion that passes within YNP boundaries has a 45 mph speed limit, and yes, the Park Rangers aggressively enforce that, due to the possibility of sudden wildlife crossings. It's going to take longer to drive that than it first appears. Do yourself a favor and top off your tank in Bozeman before heading out to West Yellowstone. There's a Costco in Bozeman, if that helps, but it doesn't carry diesel. The Costco in Billings does carry diesel.