Ah - Arches. I love that NP.

I have never ridden arches but its definitely doable. Arches and Dead Horse Point are two very popular rides in the area. For a shorter ride, definitely hit the potash road. It is flat, travels along the river, takes you past the indian hyroglyphics and has beautiful scenery. Look at me get off topic again

As for Arches, like was previously stated the steepest part is the entrance to the park. I can't remember how long the hill is but its a steady climb. Once up to the hill the main park is mostly flat with a few mild hills/rollers. I would go early and pack plenty of water.

Good luck and let us know how it goes. I am heading down that way in July and was thinking of bringing my bike to ride in the park a bit.