Almost all campgrounds that allow off road bikes or ATVs make it very clear they are to be ridden to access the trails, not ridden around camp. They are not for going between sites to visit your friends.
Many campgrounds that have no-ATV/MX rules will not allow you to unload them as they think you may try to ride or they start getting complaints, even if you don't ride them. We ran into this at a State campground in Utah while we overnighted in Ogden, host gave us a good 5 minute lecture even though I told him repeatedly that we were just passing through and staying for the night.
I agree with the others on the 2nd vehicle fee, but keep in mind that parks are lean on budgets and looking to make extra money any way they can. If you unload it they very well may try to charge you the fee. If it's an on road vehicle and unloaded they probably can charge you, they can't try to keep track of who's going in/out like the used to.