I would check the caulking around the faucet, tub spout, corners ect.
If you cut a hole in the ceiling, which you may have to do. You may first want to get an access panel to patch the hole. With the panel in hand, you will be able to cut the hole to match the panel. Cut small first, you will be going blind at this point. When you have determined where the floor joists are, you will have a better idea of where the panel should go.