Bridgeman signed for West Ham United and made his debut against Bristol Rovers on 10th October 1903. The team at the time included Tommy Allison, Matt Kingsley, James Bigden, Len Jarvis, Fred Griffiths, Charlie Satterthwaite, George Hilsdon and Herbert Lyon. In his first season he scored 4 goals in 18 games.
The teenager showed a lot of promise and Syd King signed three other forwards, Charlie Simmons, Jack Fletcher and Christopher Carrick to join Bridgeman in the forward line. By the end of the season West Ham had scored 48 goals in 34 league games. Bridgeman got 11 of these goals.
Bridgeman was less successful in the 1905-06 season, only managing 5 goals in 28 games. Bridgeman now faced strong competition for a first-team place with Harry Stapley and Billy Grassam. He also faced strong competition from Billy Bridgeman and Billy Grassam and in 1906 Bridgeman and George Hilsdon joined Chelsea in the Second Division of the Football League.
According to Tony Matthews, the author of Who's Who of Chelsea: "Billy Bridgeman was a pacy left-winger who could also play as an inside-forward. A hard-worker, never afraid to battle it outwith the tough defenders of his day, he was never considered a regular member of the side but still spent over 13 years at Stamford Bridge."
After scoring 22 goals in 160 games he moved to Southend United in August 1919.