The big boys use these guys:
Enclosed Auto Transport, Enclosed Auto Shipping, Classic Car Storage - Horseless Carriage Carriers
If you're fanatical about your car, that's the way to go. Otherwise just ship the damn thing in the open and it'll be fine. I've never seen a covered car on an exposed truck. I'm sure you'll pay extra for that as they'll have to cover and uncover the car when they shuffle them around on and off the truck.