The bunny hug was a dancing style performed by young people, in the early 20th century. It is thought to have originated in San Francisco, California in the Barbary Coast dance halls along with the Texas Tommy, turkey trot, and grizzly bear.
The bunny hug was performed to the music of America's great ragtime composers. The bunny hug, like other "animal" dances, caused a lot of uproar in polite society.
Noble Sissle has been quoted as saying that W.C. Handy's song "The Memphis Blues" inspired Vernon Castle to create the dance when he heard James Reese Europe play the Memphis blues and Castle liked the rhythm. Apparently Castle later renamed the Bunny Hug the Fox-trot, hoping to convince the public that he invented the Foxtrot dance.
The Vitagraph comedy short Bunny Dips Into Society features scenes of comedian John Bunny performing the Bunny Hug; the film was also released under the title Bunny and the Bunny Hug.
In 1914, Germany introduced a dance entitled "the rabbit dance" which was said to be just like the American bunny hug.
For an excellent example of this dance, see Barbara Boylan and Bobby Burgess on The Lawrence Welk Show episode "Strike up the Band", recorded in 1964.