There is an option if you don't mind traveling for several miles on a dirt road through Capital Reef. I driven the road but haven't ridden it on my bicycle.
In Boulder, UT take the Burr Trail Rd (1668). The road is paved until you enter Capital Reef National Park. Then is is hard packed and graded dirt. You'll come to a tee and you'll want to go right or south towards Glenn Canyon National Rec Area. In Bullfrog there is a hotel with a restaurant. Then take the ferry across the lake and follow the paved road to Hwy 95 (near National Bridges National Monument). Then go east (right) on 95 to Blanding. The road after the ferry is good and has virtually no traffic. (I've ridden it on my bike.)
I forgot to mention that you could also stay on paved roads by taking the 95 south from Hanksville and then taking 276 to Bullfrog. I've ridden this route and it was a pretty good road (276) with minimal traffic. Most of the traffic consisted of pickups pulling boat trailers. I stayed in Torrey and then rode to Bullfrog. Easily doable in one day. Just have a good water supply since there isn't much between Hanksville and Bullfrog.
The website http://www.nps.gov/glca/planyourvisit/lodging.htm
for the park says there are trailers for rent in Hite. The NPS site says there is a store at Hite that is open except for the winter season.