Hello Maria-
Indeed. It is first come/first served. There are six "walk-in" campsites in the wooded area, which have been the preferred Cycle Wild camping spot. But there's no way to guarantee that one of the six walk-in sites will be available if you show up on a weekend night.
Right now there is no official hiker/biker spot at Ainsworth, though that is in the works and hopefully we'll see it soon.
But I will tell you there is an "unofficial" hiker/biker spot at Ainsworth, the grassy spot between the two bathrooms. I've camped there even when there was other available space, and the rangers I've talked to there have been cool with it.
One thing to note about with Ainsworth: besides hearing I-84 you will hear train noise as the campground is scant yards from the UP mainline. It's not as bad as Viento, but it can bother some. Earplugs are a good idea.
-Shawn