He was born in Invercargill, New Zealand to William Bullied and his wife Marian Pugh, both British immigrants. On the death of his father, Oliver Bullied returned to Wales in 1889 with his mother. At 18, after a technical education, he joined the Great Northern Railway at Doncaster as an apprentice under H. A. Ivatt, the then CME. After a 4-year apprenticeship, he became the assistant to the railway's Locomotive Running Superintendent and a year later, the Doncaster Works manager. In 1908 he left the railway to work in Paris with the French division of Westinghouse as a Test Engineer, soon promoted to Assistant Works Manager and Chief Draughtsman. Later that year he married Marjorie Ivatt, the youngest daughter of H. A. Ivatt.
A brief period working for the British Board of Trade followed from 1910, arranging exhibitions in Brussels and Paris, but a more important change followed in 1912 when he rejoined the Great Northern Railway as the Personal Assistant to Nigel Gresley, the new CME of the railway. Gresley was only 6 years Bullied's senior.
World War I intervened; Bullied joined the British Army and was of course assigned to the rail transport arm, rising to the rank of Major. After the War, Bullied returned to the GNR as the Manager of the Wagon and Carriage Works.
Grouping in 1923 saw the GNR subsumed into the new London and North Eastern Railway, and Gresley was appointed the CME of the new amalgamated railway. He brought Bullied back to Doncaster to be his assistant, a post that was to last until 1937. This was the period during which Gresley produced the majority of his famous locomotives and innovations, and Bullied had a hand in many of them.
Among the projects Bullied was involved with were the LNER P1 2-8-2 and LNER U1 2-8-0+0-8-2 Garratt freight locomotives, and the LNER P2 2-8-2 express locomotive.
In 1937, Bullied accepted the post of Chief Mechanical Engineer for the Southern Railway (UK). At first, his work mostly involved improving the existing types, but in 1938 he gained approval to build a class of modern 4-6-2 "Pacifics", inspired by Gresley's but with all the most modern appliances. The first of the Bullied Pacifics, 21C1 Channel Packet (Merchant Navy class) was built in 1941; 30 more were to follow. A slightly smaller Pacific class for more lightly built lines followed in 1945, the West Country/Battle of Britain class, of which 110 were built; 21C101 Exeter was the first. His other major steam locomotive design, the SR Q1 "Austerity" 0-6-0 freight engine, appeared in 1942.
Bullied also played a major role in the electrification of the Southern Railway, including infrastructure, electric multiple units, and electric locomotives.
His final steam locomotive design for the SR was the unconventional Leader, appearing in 1949 after Nationalisation. This encased the boiler, coal and water supplies and everything else in a double-ended smooth body reminiscent of a diesel locomotive. Power was through two six-wheel powered bogies allowed to freely swivel with curves, each with three cylinders. The axles on each bogie were connected by gearing. The Leader was innovative but ultimately unsuccessful.
Bullied worked briefly as CME of the British Railways Southern Region but soon afterwards took a post in Ireland with the Córas Iompair Éireann (Irish National Railways) as their Chief Mechanical Engineer. He developed an unsuccessful peat-burning locomotive along the lines of the Leader which proved to be a dead end, but was also responsible for much modernisation in Ireland's locomotives and rolling stock.
He retired from CIÉ in 1958 and subsequently lived in Belstone in Devon, and subsequently Exmouth. Bullied was awarded a honorary doctorate by Bath University in 1967. Shortly thereafter he moved to Malta, where he died in 1970 aged 87.