Hi! That private tag probably isn’t correct; I just left it from somebody else’s edit. You won’t have any legal concerns biking in that area. I haven’t been in person in a while, but the only possible worry I’d think is that sections of the trail can be muddy or even submerged if it’s been raining a lot. We haven’t had any floods recently though, so unless you’re on a road bike, that whole section should be passable. Enjoy!