He attended the town's public schools, and was a three sport star at Winchester High School. In baseball he batted well over .400 and was courted by major league teams. The basketball team on which he starred won the state championship his sophomore and junior years. They moved up to the Class A (largest schools) tournament his senior year, where the team's 55 game winning streak came to an end at the hands of much larger Durfee High of Fall River. He was a dominant halfback on Winchester's outstanding football team, although his senior season was shortened by the 1955 polio epidemic.

After a year at the Naval Academy Prep School in Rhode Island, Bellino entered the United States Naval Academy in Annapolis, Maryland along with his former high-school teammate, Frank Dattilo. He was an outstanding baseball player at Navy, but his legendary exploits occurred on the football field. In his senior year, he scored 18 touchdowns while rushing and catching passes for over 1000 yards. He won the 1960 Heisman Trophy by a wide margin, garnering the most votes in each of the five national voting regions. In Bellino's final college football game, Navy's loss to the University of Missouri in the 1961 Orange Bowl, he scored his team's final touchdown with a spectacular diving catch in the end zone.

Following graduation, Ensign Bellino began his four years of active Navy service. Upon discharge to reserve duty, he joined the Boston Patriots (now the New England Patriots of the National Football League) of the American Football League, and played three seasons, primarily as a kick returner. Bellino served a total of 28 years in the United States Navy and the Naval Reserve, and retired with the rank of Captain.

Since the close of his playing career, he has been a successful businessman in the Boston area, where he has also been active in charitable organizations. He and his wife, former high school sweetheart Ann Tansey, have two children, Therese and John, and currently live in Bedford, Massachusetts.