Bishop was born in Owen Sound, Ontario. He was the third of four children born to William Avery Bishop Sr. and Margaret Louisa (Green) Bishop. His father, a lawyer and graduate of Osgoode Hall Law School in Toronto, Ontario, was the Registrar of Grey County. Attending Owen Sound Collegiate and Vocational Institute, Bishop earned the reputation of a fighter, defending himself and others easily against bullies. He avoided team sports, preferring solitary pursuits such as swimming, horse riding, and shooting. Bishop was less successful at his studies; he would abandon any subject he could not easily master, and was often absent from class.
At 15, Bishop had his first experience with aviation: he built an aircraft out of cardboard, wood crates and string, and "flew" off the roof of his three-story house. He was dug, unharmed, out of the wreckage by his sister.
In 1911, Billy Bishop entered the Royal Military College of Canada (RMC) in Kingston, Ontario, where his brother Worth had graduated in 1903. At RMC, Bishop was known as "Bish" and "Bill". Bishop failed his first year at RMC, having been caught cheating.
Bishop as an RMC cadet, c. 1914