Seems if the tile is popping off you need to fix your problem before putting down a new floor. What's below your tile? Not plywood, huh? Mortar bed? Concrete backerboard? The popping tiles seem like evidence of movement and/or an improper bond with the subfloor. I'm afraid you'll likely have to remove the tile before putting in a new floor. Depending upon the size of your bathroom you could be looking at a day of demolition and fixing of your subfloor. If the subfloor is plywood you may have some rotten areas that need to be replaced. The work required really does depend upon your subfloor type though. Once the subfloor is checked out and flat and level you could go with a quick installation of a quality vinyl flooring. The vinyl could be pre-cut long before you even start the demolition so it will install quickly.