Here's the version I learned as a child. It has a second verse.

Anna May, where are you going?
Upstairs, to take a bath
Anna May, with legs like toothpicks
And a neck like a giraffe
Anna May stepped into the bathtub
Anna May pulled out the plug
Oh my goodness, oh my soul
There goes Anna May down that hole!
Anna May?
Anna May!
(glug, glug, glug)

Anna May, how did you get there?
Did you slide down on the soap?
Anna May, don't give up patience.
Anna May, here comes a rope.
Oh my goodness, oh my soul
Here comes Anna May up that hole!
Anna May?
Anna May!
(glug, glug, glug)