Having lived for years in Oregon and Washington I learned that the best parks anywhere are in Oregon, but the state parks book full the day after New Year's Day when the reservation system opens up. There is still a chance to get in if there are cancellations.
I am not sure about biking to Bend from here unless you are a better cyclist than me but I love Cove Palisades, just 50 miles north of Bend. You drive along the high desert for a ways from Bend then make a left turn in a rather nondescript location and quickly descend in elevation to this extraordinary lake where you can rent boats and watercraft and more.
In the central part of the state I love Silver Falls State park. You would be hard pressed to find a more beautiful park, but it is very popular and I'm not sure about the size of their RV sites since I had a much smaller RV when I was going there.
On the coast my very favorite area is between Depoe Bay and Newport, OR. Just north of Agate Beach is a state park called Beverly Beach State Park which was so nice I went there at least 1X every year.
Have a great trip and be sure to have dinner at Pine Tree Tavern in Bend.
Joel