Hellyes!
A dirt bike is a light load, just make really sure that it can't hop around. I tie down the front and back with the suspension loaded, so that the bike will stay upright if one strap fails. I use a fork block (between lower triple tree and tire) to keep the load off the springs and to keep the bike from swaying, and I secure the rear wheel to the tray with a heavy duty black rubber bungee so it can't hop out (it will !)
If it's really rough terrain (4 Low) I also strap the front tire to the front of the rail, and I check the straps every 30 minutes or so. Don't expect the bike to stay upright without some sort of tire chocks or rail - even with a diamond plate floor, the tires will scoot sideways.
I drive 50+ mph on wash-boarded gravel roads, and take the rig anywhere it will fit. No problems. I do keep the two jerry cans full to provide a little ballast, but my trailer only weighs 350 pounds empty, without the lid.
An aircraft type rail tie down system is really helpful when you are hauling a bike.
The reason the bike is off center: if I am not traveling alone, I carry a couple of large Rubbermaid bins plus canopy and stuff beside the bike, strapped down with ratchet straps. If the bike were centered, the bins would not fit.
John Davies
Spokane WA