Etymological Note: So-called because a rider astride a standard bicycle is likely to have a wedgie, where underpants ride up into the crack of the buttocks.
Citations:
1993 [Morris Bisted] Usenet: rec.bicycles.soc (July 19) “Re: Recumbents (was: Is Touring Dying?)”: Great bikes (for “wedgie riders”(tm)) if you enjoy riding a bike where the leather encased saddle is wedged between the cheeks of your butt giving you that wonderful pain in your backside. 1996 Stephanie Dunnewind Columbian (Vancouver, Wash.) (Oct. 15) “Sit Back & Enjoy The Ride”: The way recumbent riders make it sound, traditional bikes are just one step up from the torture rack. One common name is “wedgie bike.” 2005 Sharon Tummins Daily News (Galveston County, Texas) (July 17) “The view from a different angle”: Last year I converted from a road bike (fondly called a “wedgie”) to a recumbent (proudly called a “bent”).