Bradford was educated at the Royal Military College, Sandhurst and was commissioned into the Seaforth Highlanders as a second lieutenant on 22 August 1888. He was promoted to lieutenant on 11 June 1890, and to captain on 3 July 1895. In 1897 he served in the occupation of Crete. The following year he took part in the Soudan campaign under Sir Herbert Kitchener, where he was present at the Battles of Atbara and Khartoum, for which he was mentioned in despatches and received the Queen's Sudan Medal and the Khedive's Sudan Medal with two clasps. He was next Aide-de-camp to Sir Francis Grenfell, Governor of Malta. In January 1900 he was transferred back as a regular captain in the 2nd battalion of his regiment, and early the following month embarked the SS "Canada" leaving Southampton for South Africa, where the battalion was to serve in the Second Boer War. He was appointed to the staff as Deputy-Assistant Adjutant-General on 3 January 1902, and received a brevet promotion as major in the South African Honours list published on 26 June 1902, with a note for future staff employment. The war ended that month, and Bradford returned to the United Kingdom on the SS "Syria" two months later, arriving in Southampton in early September 1902, when he joined the 1st battalion of his regiment.