Bauld was born in Newcraighall, Edinburgh and joined Hearts from junior side Newtongrange Star in 1946 and was immediately loaned to Edinburgh City. Upon his return, he made an immediate impact, scoring a hat-trick on his debut for the first-team. He, along with striking team-mates Alfie Conn and Jimmy Wardhaugh, became known as the Terrible Trio. He helped Hearts to a Scottish Cup triumph in 1956, the League Championship in 1957–58 and 1959–60 and League Cup successes in 1955 and 1959.