He was born in 1540 at the Vache, the seat of Edward Restwold, his mother's father, near Chalfont St Giles, Buckinghamshire.
He was the eldest son of Richard Bunny (d. 1584) of Newton or Bunny Hall in Wakefield parish, who was treasurer of Berwick, and otherwise employed in public services in the north, under Henry VIII and Edward VI; he suffered as a Protestant under Mary, and obtained some compensation from Elizabeth (16 June 1574).
[1] On 30 March 1564 he received the prebend of Oxgate in St Paul's Cathedral, in succession to John Braban.
Retaining his London prebend, with another at York (Wistow, installed 21 October 1575), and a third at Carlisle (first stall, collated 2 July 1585), he devoted himself to the work of an itinerant preacher, travelling over most parts of England, attended by two servants on horseback, visiting towns and villages, and sometimes his university, as an evangelist.
[1] Bunny published:[1] Anthony Wood makes use of A Defence of his Labour in the Work of the Ministry (written 20 January 1602, and circulated in manuscript among his friends, against the charge of thrusting himself forward as a preacher), and mentions that Bunny had translated (apparently with revisions) the Imitatio Jesu Christi.