Bradley was the first man to pitch an official no-hit, no-run game in National League history. He pitched for St. Louis in the club's victory over Hartford on July 15, 1876. The score ended 2-0 without a hit being allowed by Bradley. That same year he threw 16 shutouts over the course of the season, setting a record that has not been broken. Bradley was involved in professional baseball for thirty years, nineteen of them with the Philadelphia Athletics. He helped the A's win the championship of 1883.
He became a Philadelphia police officer following baseball. He died in Philadelphia at his home. At the time of his death he was retired on a pension from the police department which he had received beginning in September 1931. Bradley was interred at the Northwood Cemetery in Philadelphia.