It sounds like he has a leak in the building that he is blaming on you.
We were resident managers of an apartment building in Chico, CA twenty years ago and we now rent out our first house. Believe me, renters have more rights than the landlord or owner once they have given you the key (which obviously since you live there, he has:))
His threat about keeping the apartment empty is just that a threat. But I would go online and download California's tenants /renters rights. This way, you are 'up' on your rights. Even if he does start the preceedings to evict you, it will probably take all the way to the end of your lease and cost him an arm and a leg to do so. So he won't be very motivated to start legal proceedings since he seems too cheap to look into what could actually be the problem.
It is actually his responsiblity to repair and keep up his building. This should mean that he should caulk around the bathtub and seal the floor. Kinda of a 'duh' situation if you ask me. The house we have rented out has a bathroom too that might have a leak. We took out the molding and took the tile up higher, sealed and caulked everything really good and have not had a problem.
No matter how right you are in this situation, I would document everything. Take pictures of before a bath and after, document how long your showers are and how often. I don't think you are doing anything unusual. The fact is that all of the utility bills are higher now. We use less electricity but our bill amount is much more. Somehow, he is blaming this on you. You don't have to show him your documentation but if he did evict you and you did go to court, you could show the judge how ridiculous he is being.
Good luck. He can't know that water spilled on the floor when you showered so don't give him reason for thinking it did.
I just read Shane B's answer and it made me think of something else. If this does have to repair and you have to move out temporarily, I think, not sure, he will have to pay for your lodgings elsewhere. MAY be worth it to check it out. What I do know is our insurance agent realized this year that our rental was not under the right insurance. Now it is, but it cost more, but insures that we get paid (through the insurance) each month for the loss of monthly rent if our rental had a problem.