Cut the damaged drywall out. With it out inspect the area between floors to see if there's any moisture or other damage. Dry it out, run a fan, spray with mildewcide, whatever it needs. See if you can see any light shining in from the upstairs bathroom now that you have access so you can identify the source of the leak. Repair the drywall with a drywall patch then tape, mud, prime and paint.
How much water are we talking about on the floor? Did you want to see if you could turn it into a hot tub? Did you not close the shower curtain all the way and a lot of water hit the floor? Or was it something minor like you didn't use a bath mat and your feet got the floor wet?
You really need to identify the source of the water. Normally tile, even a tile job that isn't done with an underlying waterproof membrane or sealed isn't going to result in significant water seepage through the tile for most normal things bathroom floors are used for.
It's more likely there's some sort of penetration somewhere. The toilet drain (toilet base should be caulked to floor), the tub/floor joint, joints where floors meet walls, plumbing penetrations etc. Is the caulking bad in any of those areas? If so replace or add it if not there using silicone caulk.
Is the grout cracked and allowing water to pass through? If so repair the grout and seal it.
If the caulking is bad is there some reason that it's bad like the floor flexes too much when there's weight on it? If so you need to address the framing before you reseal.