Although he was never a professional footballer himself, Bradshaw was appointed secretary of Burnley in 1891, and became chairman two years later. In 1896, he became first team manager, and although the team was relegated from the First Division in his first season after finishing bottom and losing test matches (playoffs), they were promoted straight back up again the following season. Back in the top flight, Burnley finished third in 1898-99, the best position in the club's history.

In the summer of 1899, Bradshaw moved south to Second Division Woolwich Arsenal, and did the same again; after several seasons of near-misses, Arsenal finished second in 1903-04 and won promotion to the First Division, for the first time in the club's history. However, he never oversaw Arsenal at the top, as he joined Southern League side Fulham in the summer of 1904, becoming the club's first professional manager.

At Fulham, he won the Southern League title twice in succession, and won election to the Second Division at the end of 1906-07. In their first season at the top, Fulham finished fourth and reached the semi-finals of the FA Cup; however, they could not maintain their ascendance and only finished tenth the next season. Bradshaw's contract expired that summer, and he left the club to become Secretary of the Southern League, a post he held until his retirement in 1921. He died in 1924.

His son, Joe Bradshaw, played for Arsenal under his father, and went on to become manager of Fulham as well.