A fairly fun ride though I mainly go there due to its proximity to Seattle. The section between Big Finn Hill and south of QFC has some decent mostly flat trails. A six-year-old on a BMX bike can ride most of that. North of Holmes Point, there's some decent trails and some steeper terrain that is short but fun. if you go all the way down to the bottom, you'll likely end up riding in a creek. Farther south, still on the west side of Juanita Drive, there's quite a few fun cruising paths that are easy, with some technical twists here and there. The other page says "jumps in here" but I haven't really found many in there.
The map on the other page doesn't really show this, and the map on the state site isn't super clear. For the most part, in the park itself, most trails are off limits to bikes. Also, while the Arrowhead trail does offer bike access, it's a wide gravel path that a car could go down without issue.