There are so few roads in Yellowstone and Tetons. What are you trying to accomplish/see, i.e. scenery, hiking, just get through, etc.
The "traditional" routing is to follow the ACA TA to Teton Park Rd. just south of Jackson Lake Lodge, and take Teton Park Rd. to Jenny Lake (great campground, seriously one of the best) where a bike path take you all the way to Jackson.
After doing the Jackson thing (it can be expensive place to stay overnight so consider a WarmShowers host), either backtrack the Jackson Lake Lodge turn off or take US-191 (bike path to Moose, WY) to the intersection with US-26 where you rejoin the ACA route.
A third alternative, if you are willing to ride on the interstate (legal), is from Jackson, head south on US-191 to Rock Springs then head east on Interstate 80 to Rawlins. This gives you a lot more services compared to the TA route and the traffic on I-80 is really not that bad (less than a lot of large city roads) and it has a full shoulder. There are some sections of the old highway that parallel it but check out Google maps to ensure you don't ride to a dead end.
Going back to Yellowstone, if you want to see more of Yellowstone, you might consider riding to Grant Village, then do a ride over to Canyon Village then back the next day. This section has a lot of wildlife.
Tailwinds, John