If you want an alternative to Hwy 9 from Hwy 89 at Mount Carmel, from Page get to Fredonia, AZ (or if you're coming from Flagstaff you could also take Hwy 89A to Fredonia rather than going to Page); from Fredonia take AZ 389 which becomes UT59 into Hurricane, Utah and then east on Hwy 9 to Zion. This is a scenic, very pleasant drive with a RV.
From Zion to Bryce - either Hwy 9 east to 89 and north to Hwy 12 then east to Bryce.... OR.... Zion on Hwy 9 and take Hwy 9 west to I-15 then north to Circleville, UT. Pick up Hwy 20 east to 89 and then south just beyond Panguitch, UT and east on Hwy 12 to Bryce. Off I-15, Hwy 14 is very steep and curvy. Hwy 20 is the best way across from I-15.