Biddulph was born in 1840, and was the third son of Robert Biddulph. He was educated at Westminster School, and at the age of 18 joined the 19th Lancers and proceeded to India where he served in Awadh during the Indian Rebellion of 1857. Afterwards, he joined the political department of the government of British India. Between 1873 and 1874 he accompanied Thomas Douglas Forsyth, Thomas E. Gordon, Henry Walter Bellew, Ferdinand Stoliczka, Henry Trotter, and R. A. Champman on the Second Yarkand Mission - an expedition across the Himalayas to Chinese Turkestan. During this journey, Biddulph collected numerous specimens of birds and mammals, including an unknown species of Podoces which was later named in his honour by Allan Octavian Hume as Podoces biddulphi.