What type of subfloor will stand up to water in a bathroom?
First of all, you cannot assume that any flooring you install is going to be "waterproof".  That is an impossible standard in home construction, so the solution is to PREVENT water from getting to the floor surface and also to ACCOMMODATE any that does get there.

That being said, you should choose a flooring material that doesn't degrade when wet.  Tile is one choice, vinyl flooring is another, also some engineered flooring products.  Check with your local supplier for some good wet-location choices.

To prevent water from getting to the floor in the first place you want to fix the problem with your shower/bathtub so that the water is not able to be sprayed or splashed on it.  Obviously shower curtains are one cheap solution but it seems in your case that's not being used.  How about a surround that keeps the water contained in the shower/tub?

Finally as far as your underlayment, use a product that can withstand long-term water exposure.  Cement-based backer board is a commonly used product for this application.