Born in Nottingham, Beardsley started working at a government munitions factory in Chilwell. In his spare time he was a keen goalkeeper, and played for Nottingham Forest as an amateur. In 1884, he kept goal in their FA Cup semi-final against Queen's Park; the match went to a replay at Merchiston Castle, Edinburgh, which Forest lost 3-0. Beardsley was sacked by his employers for taking time off without permission, and as a result he moved to London to work at the Royal Arsenal in Woolwich. He was later joined by Morris Bates, another former Forest player.
Keen to continue playing, Beardsley soon joined a local attempt to form a football club; in 1884 he briefly played for a team known as Woolwich Union, but this side soon disbanded. After the arrival of other keen football enthusiasts, such as David Danskin and Jack Humble to the Arsenal, another attempt to form a football club followed; under Danskin's leadership they formed a works football team called Dial Square; the team would eventually become the modern-day Arsenal Football Club.
Beardsley kept goal in Dial Square's very first match against Eastern Wanderers on December 11, 1886; Dial Square were soon renamed Royal Arsenal, but Beardsley continued to guest for Nottingham Forest in matches such as FA Cup ties, and his old team-mate Bates helped as an umpire. On one trip to Forest, Beardsley and Bates managed to obtain a set of kit, giving Arsenal the red colours they still wear today.
Beardsley played for Royal Arsenal up until the 1890-91 season, when he was replaced by Edmund Bee; he played 67 first-class matches in regional leagues and cup competitions (his career predated Arsenal's entry into the Football League), and a further two FA Cup ties, including Arsenal's very first FA Cup match, a qualifying round match against Lyndhurst on October 5, 1889. He also kept goal in Royal Arsenal's Kent Senior Cup and London Charity Shield wins of 1890.
Beardsley remained an amateur throughout his playing career, and continued to work in the engineering profession; as well as the Royal Arsenal he also worked for Siemens, but was dismissed for taking too much time off to play football. Beardsley acted as a club committee member at the club during his playing career, and after his retirement from playing in 1891, he was elected club vice-chairman. He served on Woolwich Arsenal's (as they had been renamed) board of directors for the next two decades, and also worked for the side as a scout. His association with the club ended in 1910, when Arsenal fell into financial trouble and voluntary liquidation; they were bought out by a consortium led by Sir Henry Norris, but Beardsley did not join the reformed Arsenal board.
In 1913, after Arsenal had moved to Highbury, Beardsley joined the committee at Charlton Athletic, but left after a disagreement over the club's style of play (which he thought too defensive). Eventually he opened a tobacconists shop in Woolwich, on Nile Street, and lived in a house in Coxwell Road in Plumstead until his death. He died in 1939 at the age of 82.