If it is an inside wall you shouldn't have a problem. What is on the back side of the wall?
If it's the shower it could have water lines in it. Check the wall thickness the best you can, you don't want a screw coming out the other side.
Safest bet is to drill a tiny hole ( say 1/16 ) before you install a screw to see if you hit something. If you can't mount a screw there you can just fill the tiny hole with a putty stick to match your wall color. If you can't hit any solid backing use butterfly syle toggle bolts for mounting the bracket. They will hold lots of weight for their size. 1/8 or 3/16 are more than adequate for todays TV's.
2009 Newmar Ventana 3942
2010 Pace Shadow 18ft
2010 KTM 450 XCW six days
2010 Can Am Outlander 650 XT
2009 Yamaha TTR125
1989 Douglas Skater 21' Twin 2.5s
If your Bounder is similar in construction to our Minnie, I think you are going to find that the inside walls are hollow with a skin of thin plywood on both sides. Structural strength is obtained by a solid wood frame around the perimeter of the wall and a stud or two depending on the wall length. If you try to attach a TV to just the thin plywood with anchors, I think you are going to find the TV on the floor after driving over a few bumps.
IMO the best thing to do is to call Fleetwood and ask them where in the wall there is some solid structure to attach the TV mount to.