Belliss was born in Wanganui in 1951, attending (and playing rugby football at) Wanganui Boys' College. He started playing in the 1970s in the Aramaho (Wanganui) club; Joseph Romanos called him The young Turk of lawn bowls. He had been a railways fitter, and in 1982 was the first New Zealand lawn bowler to turn professional.
He has competed at four Commonwealth Games: 1982 (winning bronze), 1994 (winning bronze), 1998, and 2002; missing 1986 as a professional and 1990 as he had played in South Africa five years previously.[3]
He won the 1981, 1986 and 1992 singles titles, the 1992 and 1995 pairs titles, and the 2009, 2014/15 and 2016/17 fours titles at the New Zealand National Bowls Championships when bowling for the Aramoho Bowling Club.[6]