Okay, that's not quite the way I heard it. It's on The Best of Jim Kweskin and the Jug Band, Vanguard records VSD-79270, and the way I understand the lyrics is:

Coney Island washboard she would play,
She'd play it on the boardwalk every day,
Little soapsuds on the ground
Bubbles all around
Rub-a-dub, in her little tub
Any tune she found
Now, the thimbles on her fingers made the noise
She'd play 'Charleston' on the laundry for the boys
She could rag her way right through the knees
Of a brand new pair of BVDs
Coney Island washboard roundelay.

I always thought the song was too short and that there must be more to it - any ideas out there?