Remove all the items from the bookcase that you want to use. Flip it over so you can easily see the bottom of the bookcase.
Cut pieces of cardboard to fit on the bottom of the bookcase that touches the floor. The key is not to have any of the cardboard showing out of the bottom front.
Glue the pieces on the bottom of the bookcase. Make sure all are firmly attached to the bookcase and that the glue is completely dry before turning it back over.
Stand the bookcase back up in its normal position. Place the items back on the bookcase. Slide the bookcase in front of the Murphy bed wall. The bookcase can now be easily moved back and forth because the cardboard reduces friction.