My version I know from who knows where:

Anna Mae, where are you going
upstairs to take a bath
Anna Mae, you are so skinny
you always make me laugh
Anna Mae pulled out the stopper
to let the water out
Oh my Goodness, bless my soul,
there goes Anna Mae down that hole
Anna Mae, Anna Mae, come back up that hole! glub glub

Everyone that I tell that song to, says I made it up, I had to prove them wrong. I don't know where I learned it, I am in my 50's so it must have been a really old song. We were raised in Florida and Georgia.