Sorry if I may have mislead you - I think having to use the bus system is more of a time issue than a mobility issue.
From Bryce to Moab, I would highly recommend you take UT-12 to Torrey, then UT-24 to I-70, then US-191 into Moab. You will be going through Capitol Reef, it's worth driving down to the end and back. You should be able to do this comfortably in 1 day.
I'd also recommend that you use UT-128 to get from Moab back to I-70.
You are getting to the point where it may be worth buying an annual national parks pass for $80. Add up admissions fees for all the parks you plan on visiting. With Zion, Bryce, Capitol Reef, Arches, and Canyonlands, you are up to $75. You can buy the pass at the first park you get to.