Born the eldest son of the Rev. Edward Bowen, afterwards rector of Taughboyne, County Donegal. Educated at Charterhouse school and Trinity College, Oxford, he took a first class in classics in 1844, and was elected a fellow of Brasenose. In 1847 he was chosen president of the University of Corfu.
Having served as secretary of government in the Ionian Islands, he was appointed in 1859 the first governor of Queensland, which colony had just been separated from New South Wales. He was interested in the exploration of Queensland and in the establishment of a volunteer force, but incurred some unpopularity by refusing to sanction the issue of inconvertible paper money during the financial crisis of 1866.
In 1867 he was made governor of New Zealand, in which position he was successful in reconciling the Maoris to the British rule, and saw the end of the struggle between the colonists and the natives. He instituted the New Zealand Cross, one of the rarest bravery awards in the world, equivalent of the Victoria Cross
Transferred to Victoria (Australia) in 1872, Bowen endeavoured to reduce the expenses of the colony, and in 1879 became governor of Mauritius. His last official position was that of governor of Hong Kong, which he held from March 1883 to December 1885.
He was made a K.C.M.G in 1856, a privy councillor in 1886, and received honorary degrees from both Oxford and Cambridge. In December 1887 he was appointed chief of the royal commission which was sent to Malta with regard to the new constitution for the island, and all the recommendations made by him were adopted.
He died in Brighton on February 21, 1899, having been married twice, and having had a family of one son and four daughters.
Bowen wrote Ithaca in 1850 (London, 1854), translated into Greek in 1859; and Mount Athos, Thessaly and Epirus (London, 1852); and he was the author of Murray's Handbook for Greece (London, 1854). A selection of his letters and despatches, Thirty Years of Colonial Government (London, 1889), was edited by S. Lane-Poole.