“There is an old verb, to busk, meaning to improvise and it is from this word that busker is derived, to describe a street performer or beach singer or performer.” So says Brewer’s Dictionary of Phrase and Fable. (What's a beach singer?)
1931 New [sic] Gresham Dictionary offers: “busk to get one’s self ready, to prepare, equip, dress.” The busk was also a piece of flexible steel, whalebone or wood worn by women in the front of their stays.
Clearly just as this jongleur, braving the spring streets of Ludlow on Sunday and, forgive the expression, dropping his balls, needs more practise, so the term busking needs a little more research.