He wasted little time as he notched a then rookie scoring record with 53 goals in his first season and a total of 91 points. He followed that with another record setting 8 seasons with 50 or more goals, becoming the first player to record 9 consecutive 50 or more goal seasons. Bossy led the league in scoring in the 1978-79 and 1980-81 season and scored 60 or more goals per season 5 times, 3 of those seasons were consecutive.

There should be no doubt that Bossy could have been a ferocious scorer had back injuries not sidelined him early in his career. Bossy's playoff results are just as amazing. He was with the Islanders for all four of their consecutive Stanley Cups, scoring the Cup winning goals in 1982 and 1983, and winning the Conn Smythe Trophy in 1982, and as of the end of the 1999-2000 season ranks 6th in career playoff goals with 85.

Islanders coach Al Arbour matched up Bossy with Bryan Trottier and together the two became a potent scoring threat whenever they were on the ice. Many times Arbour talked about Bossy's quick hands, "He's got the quickest hands I've ever seen, even quicker than Rocket Richards."

Despite his short 10 year career with the Islanders he still holds the team records for the most career goals (573), most goals in a season (69), most points in a season (147), most points by a right winger in a season (147), and the most assists in a game (6). He was named to the NHL Second All Star Team in 1978, '79, and '85, the First NHL All Star Team in 1981, '82, '83, '85, and '86. He won the Conn Smythe in 1982 and the Lady Byng Trophy in 1983, '84, and '86. He also played in 7 NHL All Star Games. Bossy was rewarded for his efforts by being elected to the Hockey Hall of Fame in 1991, and his number 22 sweater hangs from the rafters of the Nassau Veterans Memorial Coliseum.