Bryce was educated at the University of Manchester, receiving his MB ChB with distinction in 1912. In 1913 he received his MD for research on stomach cancer. In 1915 he took a DPH, although he was already specialising in surgery. In 1927 he was made honorary surgeon to Manchester Jewish Hospital; this was followed by posts at Park Hospital and Salford Royal Hospital. In 1934 he was made honorary assistant surgeon at MRI. Bryce specialised in thoracic surgery, and helped establish the Society of Thoracic Surgeons, of which he was later president. He was also president of the Manchester Surgical Society in 1949/50. He established at regional centre for thoracic surgery at Baguley Hospital in south Manchester.