Born in Woolwich, south-east London, Bonds grew up in nearby Eltham, where he played for a Sunday boys' team, Moatbridge, and Kent Schoolboys and joined the groundstaff at Charlton Athletic after leaving school at 15.

Greenwood moved Bonds from midfield to the back four as centre-half alongside Tommy Taylor shortly before the end of the 1976–77 season, where he was able to come out from defence with the ball.

In 1980–81, he led West Ham to the final of the League Cup, which was lost to Liverpool after a replay, and to promotion back to the First Division.

Bonds passed Bobby Moore's club record of appearances in 1982–83 and 'officially' retired in May 1984, relinquishing the captaincy to Alvin Martin.

He was appointed Member of the Order of the British Empire (MBE) in January 1988 and was presented with the PFA Merit Award in April 1988 by his fellow professional players.

A collision with goalkeeper Phil Parkes in the last game of the 1980-1981 season broke two of Bonds' ribs, and ruled him out of selection for England against Brazil in May 1981.

He unsuccessfully applied for the manager's post when Lyall left the club in July 1989 after West Ham had been relegated.