The reason your skin gets wrinkled from being in the bathtub for too long is because your skin cells are absorbing water.
The water is absorbed through the dead keratin skin cells and when your skin absorbs the water the absorption causes the surface area of the skin to swell.
However the outer layer of the skin is tightly attached to the living tissue and in order for it to compensate for the increased surface area the skin gets wrinkled.
So in short it's due to the absorption of water into your skin and the swelling that causes wrinkled skin when in a bathtub or water too long.
If your skin begins to wrinkle in the bathtub then your skin is drying out and it's time to get out of the bathtub.