Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
BUNBURY
As described in historical dictionaries
Patronymica Britannica (1860)
BUNBURY. A cadet of the Norman house of St. Pierre accompanied Hugh Lupus, earl of Chester, at the Conquest, and obtaming the manor of_B. in Cheshire, assumed his surname from it.