Bamber was a right-handed batsman who bowled right-arm medium pace. Having previously played Second XI cricket for Middlesex and Surrey between 1976 and 1981, Bamber eventually joined Northamptonshire, making his first-class debut for the county against Cambridge University in 1982. He made a further twelve first-class appearances for the county, the last of which came against Somerset in the 1984 County Championship.
In his thirteen first-class matches, he scored a total of 638 runs at an average of 26.58, with a high score of 77.
This score, which was one of three first-class fifties he made, came against Cambridge University in 1982. He made his List A debut in the 1983 John Player Special League against Surrey.
He made nine further List A appearances, the last of which came in the 1984 John Player Special League against Somerset. In his ten List A matches, he scored 205 runs at an average of 29.28, with a high score of 71.
This score, which was his only List A fifty, came against Surrey in 1983.
He left Northamptonshire at the end of the 1984 season.