I prefer showers, but my wife likes to soak in the bathtub.....On a couple
of occasions, we have had cats who have jumped into the tub with her. It is
always a traumatic experience for both my wife and the cat.....

Yep! My sister moved from a big city to a small village, to a house
less than two yards from a channel. We kept the cat inside, but opened
a small window, 2-3 yards high to get the smell out of the house.
We should have known better.
Within seconds kitty was outside, checking out the channel.
The channel was covered in green scum, which did not look like water
to a city cat.
A duck was swimming through it, confident that no cat would dream of
jumping in....
Well, this(angora) cat, did not hesitate for a second, and attacked
that insolent duck.
The water was a bit of a surprise to him, he came out again just
half wet, and that was a very silly sight, half a very skinny cat
attached to a very fat looking dry angora half.
It took quite some time to stop laughing  :)

David submitted this idea :

My cats will always make their way up to the bathroom when I take a
bath.  Lou Lou my tortoishell used to climb around the ledge of the
bath until she fell in one time.

They always make a whining noise as if they think the water will hurt
me.  We used to have a cat called Sooty who came in the bathroom and
stood on back legs to peak in.  He saw the water and walked backwards
on only his hind legs out through the door, no kidding. lol