Barbara,
I wore shorts and a t-shirt over a bathing suit for the first part of the trip. I went swimming when we stopped at a beach and then I just put the tshirt back on for the rest of the trip. I am big about covering up in the sun, so everybody may not feel all that clothing is necessary.
We put our towels from the ship and disposable underwater camera in the compartment under the seat. That's also where I stored my shorts for the rest of the trip.