From Yellowstone to Bryce is simple to do and there are many ways to get there. I'll give you the simpliest but we'd prefer more scenery off the interstates.
You didn't state where you're staying for Yellowstone so that would make a difference, also.
If you're at West Yellowstone, take Hwy 20 south to Idaho Falls. Then I-15 through Salt Lake City. Just past Beaver, UT is Hwy 20. Take it east to Hwy 89 and go south to Utah Hwy 12. Go east on 12 to Bryce.
There is so much to see in southern Utah in the area of Bryce. It would be nice if you could do more while there.
There's Arches Nat'l Park, Canyonlands NP - Dead Horse Point State Park, Monument Valley, Capitol Reef Nat'l Park, Kodachrome State Park, Grand Canyon North & south rims, Zion.
All are easy to get to with your 40' motorhome. How much time do you have?
Have a great trip.