I don't have experience driving that kind of rig, but I've seen RVs struggling to get up (or down) and around that part of the road. I'd recommend talking to the Rangers, or maybe someone else on the Board can give you better info. The road to Cottonwood and Santa Elena is Ross Maxwell Scenic Drive; if you come in the west (Maverick) entrance to the park you'll see the intersection about half way between the park entrance and the main visitors center at Panther Junction.
The only campground I know you can get a rig that size is Rio Grande Village. Backcountry road side camp sites that you might be able to access would be Croton Springs or Government Springs on the Grapevine Hills road.
Link to the maps page of Big Bend's official site.
http://www.nps.gov/bibe/planyourvisit/maps.htm