Well, the Max Hunter site has the closest lyrics yet!

Here is the Dylan text. It’s recorded poorly, so I will leave blanks where I can’t make out the words.

There was an old lady lived by the seashore.
Bow and balance to me.
There was an old lady lived by the seashore
Number of stars there was one two three four.
Now I’ll be true to my love
And my love will be true to me.

There was a young man who...there
Bow and balance to me.
There was a young man who came...
(Someone starts talking into the tape here explaining why she can’t get it to work properly.)
The older one got...
I’ll be true to my love
As long as she’s true to me.

He gave the younger a beaver hat.
Bow and balance to me.
He gave the younger a beaver hat.
The eldest one got mad at that.
I’ll be true to my love
And my love will be true to me.

Oh, sister, oh, sister, let’s walk by the...(the tape fades away)

HTML line breaks added. --JoeClone, 5-May-02.