He was born at Beaufort, Breconshire, the eldest of three sons of William Hibbs Bevan (1788-1846), then of Beaufort, but later of Glannant, Crickhowell (high sheriff for Breconshire 1841), by Margaret, daughter of Joseph Latham, also of Beaufort, but originally from Boughton-in-Furness.
On resigning the living of Hay in November 1901, Bevan retired to Ely Tower, Brecon, where he died on 24 August 1908; he was buried at Hay, where his widow, who died on 23 October 1909, was also buried.