Bullock was commissioned into the 1st Battalion of the 11th Regiment of Foot as a lieutenant on 24 April 1872, and attended Staff College, Camberley in 1880. Promotion to captain followed on 22 February 1882, to major on 29 May 1891, and to lieutenant-colonel on 18 January 1897. He was Commanding Officer of 2nd Battalion of the Devonshire Regiment who were deployed to South Africa for the Second Boer War, and in 1902 was in command at Volksrust, where there was an internment camp for Boers. He was mentioned in despatches. The war ended in June 1902, and Bullock left Cape Town on the SS Scotin September, returning home. For his services Bullock was appointed a Companion of the Order of the Bath in the April 1901 South Africa Honours list and he received the actual decoration from King Edward VII at Buckingham Palace on 24 October 1902. Following the end of the war, he became Chief Staff Officer in Egypt in late 1902, Brigadier-General commanding Alexandria District in Egypt in 1904 and General Officer CommandingBritish troops in Egypt in 1905 before becoming General Officer Commanding the West Riding Division in 1910. Bullock was appointed Governor and Commander-in-Chief of Bermuda, a strategic colony in the North Atlantic Ocean in 1912. Bullock is remembered as moving Government House to the centre of Bermuda's social life. The British Government saw Bermuda more as a base than as a colony. Since the American War of Independence, the Royal Naval Dockyard, Bermuda had served as the headquarters of the Royal Navy in the western North Atlantic, and a large garrison, the Bermuda Garrison, had been built up to defend it. Vast sums had been spent in the 19th century on fortifying the islands, and its governors were appointed almost exclusively from the general officers of the British Army, especially from the Royal Engineers and the Royal Artillery. Bullock's predecessors had kept a distance from Bermuda's civilian population, but he made efforts to interact socially, opening Government House to prominent Bermudians and visitors, such as US President-elect Woodrow Wilson, for social functions. He also made efforts to take part in the normal social life of the colony. When Britain declared war on Germany in 1914, during the First World War, Bullock was temporarily overseas. The commanding officer of the Second Battalion of the Lincolnshire Regiment, based at Prospect Camp, Lieutenant-Colonel George Bunbury McAndrew, found himself acting governor, Commander-In-Chief, and Vice-Admiral of Bermuda in his absence, and oversaw the colony's placement onto a war footing. A contingent from the Bermuda Volunteer Rifle Corps was detached in December 1914 to train for the Front. It was hoped this could join 2 Lincolns, but when it arrived in England 2 Lincolns was already in France. it was attached as an extra company to the First Battalion instead, and was the first colonial volunteer unit to reach the Western Front when it arrived there in June, 1915. The contingent had trained at Warwick Camp, in Bermuda, over the winter of 1914-1915. As the BVRC still had to meet its obligations as part of the garrison, maintaining patrols and guarding key points around the archipelago, it did not have enough officers to provide an Adjutant to the cadre. Bullock filled this role himself, a job normally performed by a captain. The contingent, as a result, was popularly known as Bullock's Boys. Bullock retired from the governorship in 1917. Bullock also served as Colonel of the Devonshire Regiment from 1910 to 1921.
Family
He married Amy Isabella née Thomson in 1884; Lady Amy Bullock was invested as OBE for her war work on 27 March 1918.