Okay, i think the best resource i have (which you may want to see if you can track down a copy) is Vintage Hats and Bonnets 1770-1970: Identification and Values by Susan Langley. Paging through the section that covers 1810, there are a number of options for flowers and foliage on cotton bonnets--some fabric cockades, sprays of blossoms interspersed with feathers, ribbon flowers. Roses seem to be popular, as they are mentioned by name several times in the captions, though i also see several engravings featuring what are clearly morning glories, daffodils, and possibly buttercups. Hope this is of help to you!