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.