Burgess came from a strong artistic background; he was the grandson of the portrait painter, William Burgess and son of H. W. Burgess, landscape painter to King William IV. In 1848 he attended J. M. Leigh's School, London, where he met his life long friends Philip Hermogenes Calderon and Edwin Long. At first Burgess specialised in genre and portraits but after a visit with Long to Spain in 1868 he painted Spanish subjects almost exclusively.
He exhhibited widely, showing 73 pictures at the Royal Acdemy, 1850 - 96, he also showed at the British Institution and Royal Society of British Artists, London.