Surname origin
From old French bon 'good'. Walter le Bone 1296 Sussex subsidy roll.
A Dictionary of English Surnames by P H Reaney. OUP revised third edition 1997. 019860092-5.

John de Bunn,  Sussex Hundred Roll 1273.

Le Bone and Bonye existed as surnames or bye-names in South Malling in the 14th century showing the Sussex tendency to add a 'y' or 'ye' to names normally having a terminal 'e'.
The surnames of Sussex by Richard McKinley. Leopard's Head Press. 1988.
0 904920 14 3.

John BUNN(circa 1708 - 1790), blacksmith of Houghton, Sussex married firstly on the 30th September 1735 at Bury,  Elizabeth UPPERTON.  (1707 - 1736).
There were no children of this marriage.
John BUNN remarried, to Ann LUTTARD (1708 - 1780), on the 23rd May 1738 at St. Peter the Great in Chichester.
They had children:-
• Mary (1739 - 1819) = Richard EEDE (1738 -1805)
  • Anne EEDE (1775 - 1856) = John KNIGHT (1773 -1855)
    • Thomas KNIGHT (1797- 1844) = Mary AYLING (c.1801 - 1840)
    • Ann KNIGHT (1829 - 1914) =George WEST (1824 - 1904)
    • Mary Ann WEST(1858 - 1887) = George COOPER (1861  - 1941)
    • Mary Ann COOPER (1887 - 1975) = Arthur FITT (1890 - 1954)
    • Irene Mary FITT = Alfred John William COX 
• Ann (1741 - 1758)
• Sarah (1743 - 1808) = Edward VOICE ( - 1784)
  • Susan VOICE
  • Sarah VOICE
  • Edward VOICE
  • ThomaS VOICE
  • Ann VOICE
  • William VOICE
  • James VOICE
• Martha (1744)
• Elizabeth (1744 - 1753)
• Breden (1745)
• Thomas (1746 - 1813)

John Bunn was buried at Houghton in 1790 'from Walberton'.
This may be a clue to his birth.
However his daughter Sarah married an Edward VOICE of Walberton in 1765 and John may have been living with them at the time of his death.
Tantalisingly, a James BUNN of Walberton in his will of 1760 (proved 1768) makes his brother John a beneficiary.
But in the churchyard at Houghton John and his wife Ann are buried alongside three of their children, Betty, Thomas and Ann. Bookending these graves are those of Martha and John Merriott to the north and their son Richard and his wife Jane to the south. Martha was Martha Bunn the daughter of Alen Bunn, blacksmith of Houghton and possibly the sister of John Bunn.