We approached Bryce on that exact route from Green River through Hanksville, Boulder & Escalante last May. The drive was as much a highlight as any of the Nat'l Parks -- stunning & absolutely gorgeous. You'll be talking about the road just south of Boulder for a long time. It runs atop a knife ridge some hundreds of feet above slickrock views out both sides -- early training for Dead Horse.
There are some wide pullouts to enjoy the view. There won't be much for fueling stops northeast of Torrey/Capitol Reef until you get to Green River. Enjoy the drive!
Some pics between Bryce & Green River. First, a couple south of Boulder...
North of Boulder going over the pass in Dixie Nat'l Forest...
Capitol Reef...
Random roadside scene north of Hanksville...