We don't have synonyms for bunnet yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are bonnet, punnet and bennet.
(n) :
a bunnet or bunnit is a specific style flat sporting cap made from wool or a wool blend that is common with farmers and country gentlemen in cooler areas of the planet that experience higher than normal rainfall such as Scotland (where it originated), the British Isles, New Zealand etc. The bunnet is light, warm and comfortable; a flat cap, traditionally made of wool
(n) :
a bunnet or bunnit is a specific style flat sporting cap made from wool or a wool blend that is common with farmers and country gentlemen in cooler areas of the planet that experience higher than normal rainfall such as Scotland (where it originated), the British Isles, New Zealand etc. The bunnet is light, warm and comfortable; a flat cap, traditionally made of wool