Thanks for the question! I biked the Willamette Valley Scenic Bikeway in 2011 (read my blog from the ride) and it was one of the best trips I’ve ever been on. I rode in the opposite direction you’re planning, finishing the ride at Champoeg State Park. Champoeg State Park offers RV spaces that you can reserve online.
One of the best resources for this route is rideoregonride.com. You can see all the latest about the trip and also see where the closest bike shops, restaurants and lodging are located along the way.
As for transportation from Armitage Park near Eugene back to your RV at Champoeg, the options are limited and there isn’t one point to point option. What I recommend is to take the Amtrak Cascades from Eugene to Salem. For an additional fee you can bring your un-boxed bike on board The only downside to taking the Amtrak Cascades is that you can only get as far north as Salem. From Salem it’s around 30 miles to Champoeg State Park so you would have to either get a taxi or use pedal-power to get you there.
I hope this helps. Let me know if you have any other questions.