Bundy was born in 1861 in New Castle, Indiana. He graduated from the Military Academy in 1883, and served on the American frontier, participating in the Indian Wars campaigns against Crow and Sioux Indians. During the Spanish-American War he fought with the 5th Army Corps in Cuba, and received the Silver Star for gallantry at the Battle of El Caney. From 1899 to 1902, he served in the Philippinesduring the insurrection and subsequently, after teaching law at Fort Leavenworth, Kansas, participated in the Moro Expedition in the Philippines in 1905–1906. Bundy served within the United States until 1917, where he commanded a regiment on the United States–Mexico border.
In 1917, he assumed command of the 1st Brigade, 1st Expeditionary Division, and in June he sailed for France. As a division and corps commander during World War I, he participated in the occupation of the Toulon and Troyon Sectors near Saint-Mihiel, served in the Aisne-Marne operations, and took part in the occupations of Chateau-Thierry. Following the war, he commanded Fort Lee, Virginia, the 7thCorps Area, the Philippine Division, and the 5th Corps Area.
For his services in World War I, General Bundy was awarded the French Legion of Honor, Commander, and the French Croix de Guerrewith Palm. However, his bravery in battle has never been officially recognized by the U.S. government. Bundy retired in 1925 and died inWashington, D.C. in 1940.
The USS General Omar Bundy (AP-152), launched August 1944, was named in his honor.