This is the route recommended from Grand Canyon South to Bryce (& I assume you're staying at Trailer Village in the park itself). If you're staying elsewhere you'll have to adjust.
Grand Canyon - Trailer Village - take Hwy 64 east out of the park to Hwy 89.
Take Hwy 89 north and just north of Hwy 160, continue on 89 and you'll be directed to a very easy detour because of a road collaspe about a year or so ago on 89. This detour will take you into Page, AZ.
From Page follow 89 west to Kanab, Utah.
From Kanab take 89 north to Utah Hwy 12 which is just south of Panguitch, UT.
Take Hwy 12 east to Bryce.
This route is 282 miles. A good stopping point for stretching would be Page, AZ and you might even consider spending the night to check out Glen Canyon lake in town. There are no big climbs or switchbacks on this route. At 50 mph this would be approx. 5-1/2 hours of driving time - no stops.
Alternatively, drive the same as above but when you take 89 to the detour you'll instead pick up 89A to Jacob Lake, AZ and Kanab, Utah. Then you'll pick up 89 north again to Hwy 12. This bypasses Page, AZ. This route is 276 miles but you'll have a very steep climb with switchbacks on 89A just before Jacob Lake. We've done it often with our motorhome but just wanted to alert you.
There's not much mileage difference between the two routes - just depends on what you want to see along the way.
Ruby's RV is recommended for touring Bryce if you want hookups. It's just outside the park entrance.
Have a great trip.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel