The outside or inside of the bathroom?
I looked at some of the past Scamp* bathroom door postings and it looks like they use a piano hinge and fairly thick wood, so it should be able to support an LCD TV. Probably a good idea to use stainless hardware on the inside if you have a shower inside.
I'm guessing you want to be able to swing out the door/TV to face the bed or dinette?
If you have some space elsewhere you might consider rather than a flat or semi-articulated mount on the door, instead get a cantilever mounting that will go on a bulkhead if you have space. I used this one mounted to the bulkhead in my Escape-19 because it can swing out to face either direction and you can lock the LCD down for travel or remove it entirely fairly quickly.
Master Mounts LCD Locking Cantilever Mount | Wayfair
You pull the chain and open the hinge to fold it out, and you can lock it back with the mount folded back into the main hinge.