Educated at Trinity College, Cambridge, Bulwer was commissioned into the Royal Welch Fusiliers in 1849. He served in the Crimea War and took part in the Battle of Alma in 1854. He then took part in the Relief of Lucknow during the Indian Mutiny. He was appointed Assistant Inspector of Reserve Forces in Scotland in 1865, Assistant Adjutant-General for Recruiting in Scotland in 1870 and Assistant Adjutant-General for Auxiliary Forces at Army Headquarters in 1873. He went on to be General Officer Commanding Chatham District in 1879, Inspector-General of Recruiting at Army Headquarters in 1880 and Deputy Adjutant-General to the Forces in 1886.