Appointed conductor of the Royal Philharmonic Society of Sydney in 1908, Bradley arrived with his wife on 23 March in the Somerset. With the Philharmonic Choir and the new Sydney Symphony Orchestra, which he also conducted (always without a baton), in 1908-14 In Bradley's twenty years in Sydney he conducted 126 performances including 29 of the Messiah, 8 of Mendelssohn's Elijah, 5 of Haydn's The Creation, 4 of Berlioz's La Damnation de Faust and 4 of Elgar's Caractacus. Conforming with the style of the society, his performances were safe rather than adventurous.
Verbrugghen was chosen in preference to him as first director of the new State Conservatorium of Music, but Bradley philosophically accepted the professorship of theory and later also taught solfeggio. He published A Solfeggio Manual for Teachers (1919) and A Manual of Musical Ornamentation (1924). He was one of three conductors for the opening concert of the conservatorium in 1915 but, being bald, rotund and impassive, he seemed stodgy compared to Verbrugghen. Though dreaded by students as something of a martinet, he was recognized by all as peerless in theoretical and practical musicianship.
When Verbrugghen resigned, Bradley was on the committee which governed the conservatorium in the interregnum, then in 1924 went on a short visit to Europe, partly to introduce Gladys Cole, a favourite singing pupil, to the musical world. Soon after his return his eyesight began to fail. Pugnaciously proud and reserved, he told nobody, not even his wife, conducted from memory as long as he could and resigned without explanation only when faced with a new score. The Philharmonic Society was angered and gave him only a lukewarm farewell and a meagre cheque. He returned to England in January 1928 to join his son Julius who had spent years in China. An operation for a cataract left him blind. Aged 78, he died of cerebral vascular disease at Harrow, Middlesex, on 3 March 1935.