Henry Bryden was born on 3 May 1854 in Banbury, the third son of William Anderson Bryden, and Maria, daughter of William Cowper. He attended Brackenbury's Anglican Preparatory Military Academy and went on to study at Cheltenham College, leaving in 1869.Cheltenham College Register, p.288, 1841-1910. (1911). United Kingdom: Bell. At Cheltenham at the same time were his two older brothers, William Radford Bryden the architect, and Charles Bryden, also a future England rugby union international. As well as rugby football, Henry was known as an excellent long-distance runner, and holder of 37 prizes. He represented South versus North of England, and was second to Walter Slade in what was at the time the fastest amateur mile on record (time 4m 24.5s) in 1875.
