How do I fix a leak in the bathroom floor?
Seal the floor with a high quality penetrating sealant.

Another way to fix this would be to take up the entire floor and redo it, ensuring the floor is solid enough it won't bend and cause cracks to form. However, sealing it should work. 

Keep in mind that such a leak may be behind the wall along a pipe to the shower head or some other place where a leak is possible. In that case it would follow the pipe back down and enter the subfloor via that route.

You can get a special camera at the home improvement store to look through a small hole to inspect for leaks rather than having to tear open the wall. This way you should be able to locate the actual path of the leak without having to tear up the bathroom in the process. If possible, enter the wall from an adjoining room rather than making a hole in the tiled walls of the bathroom. It's a bit easier to repair a small inspection hole in sheetrock than it is to replace a tile.

If you have grout that is not sealed then water can pass through the grout almost like passing through sand. Seal it.