I recently bought Denise Drehers book "From the Neck up - An Illustrated Guide to Hatmaking". There are three patterns for mid-century bonnets in that book , but the brims look like they make up most of the bonnets. You are lucky because the only library in Sweden to have this book is Stadsbilioteket in Gothemburg. It is marked "referens" and can be found in the section Qcca. Looking at Google pictures I searched for bonnet 1850 and got some pictures of bonnets from different angles, both reproductions and from the era. Good luck!
Johanna