(NB: As of now, these are all from the Met. I find their online collection database to be the largest and easiest to sort by date, which is why most of my museum research posts are based there.)
First, paintings and drawings. You can magnify most of them when you follow the link, and zoom in on the
Woman with Lilacs and Eggs, Chardin, 1725-1750
The Strong Family, Charles Philips, 1732
Card Players in a Drawing Room, Dumesnil the Younger, 1740s
Double Portrait, Charles Antoine Coypel, 1743
Study of a Woman, Joseph van Aken, 1740-1760
The Letter, Pietro Lunghi, 1746
Girl Building a House of Cards, Thomas Frye, ca. 1750
Serving Girl Knitting, André Buoys, ca. 1750
Florentine Woman in a Butterfly Cap, Jean-Baptiste Greuze, 1755
Broken Eggs, Greuze, 1756
A Dance in the Country, Giovanni Domenico Tiepolo, 1755
Portrait of a Woman, Johann Nikolaus Grooth, ca. 1760
It looks to me like it was most common for women to wear caps with two defined, symmetrical ruffles, or one that sort of dips in at the top of the head. The higher the social class, the more hair could be shown in front. Though some have ribbon bows that wrap around the head, others don't appear to.
Second, extant caps. It's difficult to separate babies' from adults' (or those of children who are old enough to be dressed like adults) when they're photographed flat, but I think I found some women's caps. I date them to roughly the right time period based on the paintings - most of what comes up when you search for caps were accessioned in the early twentieth century, before people began studying costume history in a serious way, and there's no attempt to date them beyond their century. In worst-case scenarios, they're labeled "1700-1945".