Hi LuvsGolden and welcome to the Jayco Owners Forum!
We experience the opposite with our mattress as it fits so tight between the "end tables" on our model tt that it's hard to move it by myself to put on the fitted bottom sheet. Is your mattress thin? Ours is pretty thick, so it stays put. Also, (sorry, I know this may sound like a silly question) but did you remove the plastic from around (or under) the mattress? Without endtables to keep the mattress in place, the plastic wrap could provide a slick surface so the mattress would slip.
As for the bedspread, we stow ours and use a comfortor instead. It stays put better than the bedspread that the tt came with.
Hmmm, here's another thought, lotsa folks get those 1-2" toppers for their mattress. They are pretty heavy, so maybe that would help it stay in place?