Bulgin, a fullback, began his career with Eastern Suburbs club as a 19-year old in 1947.
The following year he was selected for NSW on their tour of New Zealand and later that year went away on the 1948–49 'Kangaroo Tour'. He appeared in 16 matches on tour, – no tets. In 1949 Bulgin again went away with the Australian rugby league side on its tour of New Zealand, once again though he never played in any of the test matches.
In 1950, he joined the Canterbury Bankstown club where he played for two seasons. In 1951 he captain-coached the club.
While playing football, Bulgin also served in the New South Wales Police Force and in 2008, rugby league's centennial year in Australia, he was named at fullback in a NSW Police team of the century.