Not wearing a bonnet; without a bonnet; bare-headed.
From 'bonnet' plus the negation suffix '-less', forming an adjective that means the absence of a bonnet, used from at least the 18th century in descriptive texts.
A 'bonnetless' woman in Victorian writing would have been shocking—it's not just saying she didn't wear a hat, it's emphasizing a social transgression, showing how much clothing choices encoded respectability!
Complete word intelligence in one call. Free tier — 50 lookups/day.