Bradley was born at Clapham, Surrey, England (now part of the Greater London area). He was the child of Charles Bradley, an evangelical preacher, and Emma Linton, Charles's second wife. A. C. Bradley was his brother. Educated at Cheltenham College and Marlborough College, he read, as a teenager, some of Immanuel Kant's Critique of Pure Reason. In 1865, he entered University College, Oxford. In 1870, he was elected to a fellowship at Oxford's Merton College where he remained until his death in 1924. Bradley is buried in Holywell Cemetery in Oxford.