His education, like that of his two brothers, Francis, who became eventually 9th Duke of Bedford, and Arthur, who sat for a generation in the House of Commons as member for Tavistock, was carried on entirely at home, under the general direction of his mother.
In March 1849 Odo was appointed by Lord Malmesbury attaché at Vienna. From 1850 to 1852 he was temporarily employed in the foreign office, whence he passed to Paris. He remained there, however, only about two months, when he was transferred to Vienna. In 1853 he became second paid attaché at Paris, and in August 1854 he was transferred as first paid attaché to Constantinople, where he served under Lord Stratford de Redcliffe. He had charge of the embassy during his chief's two visits to the Crimea in 1855, but left the East to work under Lord Napier at Washington in 1857. In the following year he became secretary of legation at Florence, but was detached from that place to reside in Rome, where he remained for twelve years, until August 1870. During all that period he was the real though unofficial representative of England at the Vatican, and his consummate tact enabled him to do all, and more than all, that an ordinary man could have done in a stronger position.