I remember this story too - it was one of my favorites in grade school - they used to have a flim strip of the story that they'd play for us once and a while.
I can remember a couple songs that were part of the story - "Doodley-doodle, doodley-doodle, she lived in a vinegar bottle", and "little fish, little fish, I have a wish".
The old woman would go to the little stone bridge over the creek and recite the "little fish" ditty, and then the fish would appear and grant her a wish.
I'm struggling to remember the rest, but in this information age, we've got to be able to find out more.
My fiance thinks I am ridiculous for even caring about this, but for some reason I recalled that "vinegar bottle" song the other day, and I began searching for information - that's how I came upon this thread.
Good luck!