Of movement, I would think that a top quality silicone caulk would be a good choice. It is flexible and should adhere well to the tile and tub.
Use masking tape to outline the edges of where you want the caulk. Fill in the area and smooth it out with your thumb or fingers. Remove the tape before the caulk sets.
Of course, if you are talking about 1/8 inch of movement, you will need to do something to stop that before caulking.