As far as I can tell, the WA hiker/biker fee is $14, which is definitely a lot steeper than Oregon's $5. However, the $14 is per site, not per person, so if you had 3 or more people in your group, it would work out to being the same price or cheaper than Oregon.

The Washington state park website doesn't seem to list hiker/biker sites, it just lists "primitive" sites. So it's harder to tell if a park has specific bicycle sites. The park host or ranger might give you the "bicycle" rate for a regular site if you show up and there isn't a specific bike site available. However if you book online it's not going to do that (plus there's that whole reservation fee.)

I camped at Bay View in 2005. The website listed a bicycle site, but when I arrived the ranger said they removed it to make room for cabins. (I don't know if they've made a new hiker/biker site since then.) Since all the regular sites were full, he let me camp in the picnic area. Given the choice, I would've ridden the extra 15 miles or so to Deception Pass, (the view from Bay View is an oil refinery) but I wouldn't have reached Deception until after dark.