early 15c., "kind of cap or bonnet worn by men and women," from Old French bonet, short for chapel de bonet, a cap made from bonet "kind of cloth used as a headdress" (12c., Modern French bonnet), from Medieval Latin bonitum, bonetum "material for hats," which is perhaps a shortening of Late Latin abonnis "a kind of cap" (7c.), which is perhaps from a Germanic source. (If that is correct, a chapel de bonet would be etymologically a "cap made of cap").
As a form of head-covering worn by women out-of-doors, bonnet is attested from late 15c. As a type of mechanical covering device, by 1862.