Yes, Abigail Adams wore bonnets—routinely. In the 18th century, a bonnet was not optional adornment; it was essential equipment for women of every class.
As a farmer's wife, diplomat's spouse, First Lady (1797–1801), and prolific letter-writer (1,100+ to John), Abigail managed households in Braintree, Philadelphia, New York, Washington. Her bonnets appear in portraits (e.g., 1795 Stuart) and invoices: "1 Leghorn bonnet, 2 cotton caps, 3 yds ribbon." She complained of Washington dust ruining straw; praised Philadelphia milliners.
The bonnet framed the face that argued for women's education ("Remember the Ladies"), managed a farm alone for years, and negotiated political intelligence. It was the helmet of a citizen-mother in the early Republic.