Born in Virginia City, Nevada, Bulmer graduated from the Naval Academy in 1894. After World War I, he served as United States naval representative at a conference which met at the British Admiralty to consider clearing the seas of mines after the war. On 5 January 1919 he assumed command of that operation. His zeal and courage, combined with a sound knowledge of his profession, contributed greatly to the success of the mine force.
The destroyer USS Bulmer (DD-222) was named for him.