I never actually did this dance, and don't even remember what it looked like, but I must have seen it on "American Bandstand." I remember the popular song. Lyrics found on the Internet and corrected by me based on the mp3 file.

THE BRISTOL STOMP
[Words and Music by Kal Mann and Dave Appell]

CHORUS: The kids in Bristol are sharp as a pistol
When they do the Bristol Stomp.
Really somethin' when the joint is jumpin'
When they do the Bristol Stomp.

1. The sounds are spinnin' every Friday night.
They dance the greatest since they do it right.
But here's the latest--it's a crazy sight to see. CHORUS

2. It started in Bristol at a deejay hop.
They holler and whistle, never want to stop.
We pony and twist it and we rock with Daddy G. CHORUS

BRIDGE: It's got that groovy beat
That makes you stomp your feet.
Come along and fly. Wanta feel fine.
Then once you dance with me,
You'll fall in love, you'll see.
The Bristol Stomp will make you mine, all mine.

(Repeat 1, CHORUS, 2, CHORUS)

Click to play. (That mp3 file comes from a web site that looks promising: The Doo Wop Jukebox – but I had to view their source code to figure out how to construct the URL.)

More info from Wikipedia:

The Bristol Stomp was a song written in 1961 by Kal Mann and Dave Appell, two executives with the Cameo/Parkway record label, for the Dovells, an a capella singing group from Philadelphia, Pennsylvania, USA, which recorded the song for Cameo/Parkway late that year.

The song made the 37th spot on the Billboard magazine pop chart in 1962.

The song was written about teenagers in 1961 who were dancing a new step called "The Stomp" at dances held in a fire hall in Bristol, Pennsylvania, a small industrial borough outside of Philadelphia.