Front View: The fabric on the brim is very tightly gathered. You can also see that there is a line where the fabric was gathered towards the end of the brim.
Side View: There are more lines where the fabric was gathered along the side (By looking at this picture, there are three on the outside of the brim. The crown seems to be gathered more tightly at the top than at the bottom.
Back View: Under the crown on the brim there is a bow where the bonnet ribbons are attached to the bonnet.
Back/Side View: You can see a little more details with the bow here.
This bonnet is worn with various outerwear. Above, there were pictures with the travelling pelisse and one with the brown spencer.
Here's the front view with the brown spencer.
In one scene, we see Elizabeth wearing this bonnet with the black spencer.