Bob Swift's journey in professional baseball began when he was signed by the St. Louis Browns in 1938. However, it was with the Detroit Tigers that he spent the majority of his playing career, establishing himself as a reliable catcher. Swift's tenure with the Tigers spanned from 1944 to 1953, during which he became known for his defensive skills behind the plate and his ability to handle pitchers effectively.

Swift's career was interrupted by World War II, as he served in the United States Army from 1943 to 1945. Upon returning to baseball, he quickly resumed his role with the Tigers. Although not known for his offensive prowess, Swift's defensive capabilities were highly valued. He was adept at managing the game from behind the plate, earning the trust of his pitchers and coaches alike.

In 1953, Swift was traded to the Boston Red Sox, where he played for a brief period before moving to the Philadelphia Phillies. His playing career concluded with the Phillies in 1957. Throughout his time as a player, Swift was recognized for his steady presence on the field and his leadership qualities, which would later serve him well in his post-playing career.

After retiring as a player, Swift transitioned into coaching and managing. He returned to the Detroit Tigers as a coach, where he worked under manager Jack Tighe. Swift's understanding of the game and his ability to communicate with players made him a valuable asset to the coaching staff. In 1965, he was appointed as the interim manager of the Tigers following the departure of Chuck Dressen due to health issues. Swift managed the team for part of the 1965 season and into 1966, demonstrating his capability to lead at the major league level.

Unfortunately, Swift's managerial career was cut short due to his own health challenges. He was diagnosed with lung cancer in 1966, which led to his untimely passing later that year. Despite the brevity of his managerial tenure, Swift's influence on the players he coached and managed was evident.