A bonnet was a type of headgear that was common on Earth.
In 1893, the maid at Guinan's house wore a bonnet. (TNG: "Time's Arrow")
In 1996, Kes and Neelix were monitoring media broadcasts from Earth and on one of many television channels, they saw a young girl that was wearing a bonnet. (VOY: "Future's End")
In 2155, baby Elizabeth wore a white bonnet. (ENT: "Terra Prime")
In an alternate version of 2259, a couple women walked past the Kelvin Memorial Archive, one of which was wearing a black bonnet and the other was wearing a white one. (Star Trek Into Darkness)
In 2381, a worker at the Boimler family vineyards wore a sun bonnet. (LD: "Grounded")