Born in Slough, Berkshire, Busby started his playing career at Wycombe Wanderers in 1966, but was unable to hold down a regular place in their team, despite his emerging talent. He moved to Luton Town in January 1970. At Kenilworth Road Busby scored four goals in his first nine matches helping the club gain promotion to the Second Division in 1969–70. He scored eight goals in 1970–71 but struggled to find form in 1971–72 and spent time out on loan at Newcastle United. He was sold to Fulham in August 1973 where he had the most prolific spell of his career. He scored 12 goals in 1973–74 and 18 in 1974–75 of which six were in the FA Cup helping Fulham reach the 1975 FA Cup Final, losing 2–0 against West Ham United. After scoring 38 goals in 155 matches for the Cottagers, he moved to First Division Norwich City where he made a fine start scoring 11 goals in his first 18 matches for the Canaries.