I don't know which direction your loop is, clockwise or counter, but it looks like the Jackson-Cody portion uses Hwy 14. I offer the following alternative in that area. Use Hwy 212 to enter/exit Yellowstone so you can detour up to Red Lodge via Beartooth Pass. It's awesome. Then turn around and ride it the opposite direction and use Hwy 296, the Chief Joseph Hwy, to ride down to Cody. You won't be disappointed. See route below: