It seems that family tradition among some people who have this last name is that it comes from the way their infants move around. Unlike most children who crawl before they walk, many Shufflebottoms are supposed to sit on their bottoms and pull with their legs. In America we usually call this behavior butt-scooting, but in England it is often bum "shuffling."
To try to figure out if this behavior is the origin of the name, the researchers interviewed people with the name Shufflebottom and asked about how their children got around as infants. In a clever comparison, they also asked a similar number of people with the surname "Walker" the same questions. They found no difference in the rates of shuffling between the two groups.
The authors of the study gave a few explanations for why their results might not have supported the family tradition. One possibility is Shufflebottom infants may have shown this behavior a long time ago, but crawling may have become more common after many generations of marrying other families that did not favor this behavior. The article also addresses the possibility of a different origin of the surname altogether.
Full Article Citation:
Fox, A. T., Palmer, R. D., & Davies, P. (2002). Do “Shufflebottoms” bottom shuffle? Archives of Disease in Childhood, 87(6), 552 -554. doi:10.1136/adc.87.6.552