WA state law provides no bicyclist will be turned away from a state campground and accomodation must be found for the bicyclist. they'll get you a spot if you make enough fuss, but go check the sites first, always, before going to the office or paying the fee.
just roll right in, and look for the walk in sites. claim any unreserved spot. barring that, roll thru the car camping sites and take any unreserved spot. if all spots are taken or otherwise reserved, THEN check at the ranger station. at Worden it's in the old barracks, at Old Fort Townsed SP there is only a self pay box.
I've had NO problem finding spots in the walk in sites at Old Fort Townsend State park, just up the hill south of Port Townsend.
even at Fort Worden, I'd check there first. Ride in thru the gate, the walk in camping is about 200 yards straightaway, and then look to the left, past some old barracks and the little fuel depot. past another row of housing there to the upper campground, then to the left again to the southern end of that for the hiker/biker sites. just roll in and claim a spot.
Fort Worden is the coolest. much, much cooler than any other camping around. "an officer and a gentleman" was largely filmed there. lots of cool bunkers, tunnels, gun emplacements, museums, coffee shop, beach, wahrf, history just seeping out, etc...
but even Old Fort Townsend (not much fort, a lot of old) is just a 2 mile uphill ride past the last grocery store at the bottom of the hill.
you could always camp near the cemetary by Fort Worden
- go to the gate, and then to the left...
check it out, therabouts....
you'll like staying in Port Townsend rather than Whidbey. there is little to do on the Whid at night, and a lot of neat stuff in Port Townsend, including live music.
check out the old Town Tavern at night, and definetly grab a slice from the pizza window downtown during the day.