Evens was born in post-war Plymouth, where he lived until he was six. His father joined up with the Devonshire Regiment at the beginning of World War II and then entered banking once the war was ended. His career meant a number of moves for the Evens family, including a period in Exeter, where Robert attended Hele's School, and a later move to Ilfracombe.
Robert followed his father into banking, working at National Westminster in Barnstaple and later in Bristol and Bath, before training for ordination to the priesthood. He was ordained deacon in 1977 and priest in 1978. Evens was previously Archdeacon of Bath in the Diocese of Bath and Wells from 1996 until his consecration to the episcopacy. Bishop Bob was consecrated bishop at Westminster Abbey on 30 November 2004 and installed as Bishop of Crediton on 5 December 2004 at Exeter Cathedral; he retired on 31 October 2012.