Growing up in St. Paul, Bob Paradise was a big lad who excelled at a number of sports. He earned all-state honours in football and hockey. He also turned down a professional baseball contract from the Boston Red Sox in 1965 so that he could complete his education at St. Mary's College. While at the school, Paradise continued to develop his hockey skills, becoming an all-conference performer in the Minnesota Intercollegiate Athletic Conference for four consecutive years.
He turned pro in 1966 and embarked on the journeyman's path to the NHL via numerous teams and leagues from the U.S. Olympic squad to the Montreal Voyageurs of the AHL. In 1971, Paradise saw a sliver of NHL action with the Minnesota North Stars before heading back to the minors for more seasoning. While he was skating for the Cleveland Barons of the AHL, the expansion Atlanta Flames purchased his services in 1972. The move finally gave Paradise a regular shift at the NHL.
He sustained his presence with the Flames as a defensive-minded blueliner who engaged a physical style of play not unlike his father-in-law, former New York Ranger and U.S. Hall of Famer, Bob Dill. Paradise continued in his role as a conservative defender through stints with the Pittsburgh Penguins and the struggling Washington Capitals. In 1977, the Caps sent him back to the Pens where he rounded out his NHL career in 1979.