Buy a mattress that has 1 side for sleeping and 1 flat side that goes face down to decrease mattress slippage.
Mattress that moves up and down.
Move the bed off to the side and place the rug on the floor.
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As the bed moves so does the mattress.
Lift the bed frame up at each corner and slide the pieces of rubber liner underneath.
To move a mattress by yourself try to fold it half width wise and secure it in place with 2 or 3 ratchet tie down straps.
There many types of adjustable beds there are ups which are often wired remote bases that only move your upper torso and head up and down starting at usually 500 for a queen.
All control wands adjust the head and foot of the bed up and down at the touch of easy to use buttons.
You mention your need for an adjustable bed is related to a physical health issue.
Once your mattress is in a more compact shape stand it on one of its ends and lift it up onto a dolly.
Using a remote control the motor of the bed moves both the upper and lower portions of the bed up and down via a remote control.
Get an area rug that is slightly bigger than the area the bed covers.