There is a helpful little file here for developing a better understanding of late 50s & early 60s millinery. Use it alongside browsing museum collections.
https://annaworden.wordpress.com/welcome/pdf-pages/
Anatomy of a Bonnet
If I Had My Own Blue Box:
Adventures in the Nineteenth Century, and maybe a little beyond — Anna Worden's Blog
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If I Had My Own Blue Box: 
Admittedly, these bonnets are some years back in my work. So, there some bits that are off.