William R. Scott qualified as Doctor of Medicine (MD) at the Royal University of Ireland in 1885. After further studies at Queen's Colleges, Belfast, and at Dublin, he qualified as Master in Surgery (MCh), Master in Obstetrics (MAO) and Licentiate of the Apothecaries' Hall of Dublin (LAH) in 1887. For some time he was an assistant surgeon at the County Infirmary of Monaghan, Ireland, and surgeon to the Belfast Ship Yard. By 1895 he had settled in Bloemfontein and was licensed to practice in the Orange Free State (now the Free State) on 17 September 1897. Subsequently he served as medical officer of the Board of Health. In 1897 he contributed two articles to the South African Medical Journal, one on "Boric acid", the other on "The small-pox epidemic in Bloemfontein".
In 1899 Scott took over from Reverend Dr John Brebner* the task of making meteorological observations at the only second order meteorological station in Bloemfontein, and supplying the results to the Cape of Good Hope Meteorological Commission. The commission published a summary of his results in its report for 1899. However, no results from Bloemfontein were published during 1900-1902, presumably as a result of the disruption caused by the Anglo-Boer War (1899-1902).
In 1901, after the Free State had been occupied by the British, he complained to the administration of the new Orange River Colony that his post as medical officer of health for Bloemfontein had been given to another doctor, and applied to be appointed as resident medical superintendent of the leper asylum. He was still practising in Bloemfontein in 1916.