If you follow the Trans Am route, ride Yellowstone early as the map suggests. The traffic can be horrible. And when I was there 9 years ago, there were no shoulders on some busy roads, including the road between Yellowstone and Teetons. Hope they have improved things since then.
I think day of the week may matter too, but we didn't find the traffic all that bad. We entered the park late in the day on Sunday and I suspect that most of the weekenders had left. Folks who were there on Saturday said it was pretty bad.
There is a good chance you will have to stop in Jeffrey City, WY. Somewhere at this forum a traveller who stayed at the motel in town had mushrooms growing in his carpet.
If you are camping you can stay in the old abandoned Lion's Club Pavilion in Jeffrey City. A nice roof and flat concrete surface with tables is all it has, but the restaurant across the street has rest rooms and water and they will point out the pavilion. The town is nearly a ghost town, so I'd say give the restaurant some business. We bought drinks there and bought breakfast in the morning, but cooked our own dinner.
BTW just buying the AC maps and figuring it out as you go worked very well for us. I'd say to be familiar with your gear, pack carefully, and pick an appropriate departure time, but once on the road pre-planning is pretty unnecessary especially with the AC maps.