His prolific scoring propelled the Islanders to four consecutive Stanley Cups (1980-83) and earned him the Conn Smythe Trophy in 1982. His 85 playoff goals was a league record when he retired. As gentlemanly as he was prolific, he received the Lady Byng Trophy three times (1983, 1984, 1986).
Bossy suffered a back injury during his 10th season in the league (1986-87) that hampered his play and reduced his playing time. He retired after the season, the only year he did not score 50 goals. He was inducted into the Hockey Hall of Fame in 1991. He remained a staunch advocate against rough play on the ice. In 2006, he was named the New York Islanders' Executive Director of Corporate Relations. He died of lung cancer in 2022 at the age of 65.