You will need: A steam iron, ironing board, cotton scrap to serve as a barrier, and a wig head.
First, take the squished brim, and iron using the cotton scrap as a barrier with high steam to dampen and heat up the buckram. Once the buckram is soft and pliable, roll the brim while you move the iron over it to re-shape the brim.
Once's it's been re-shaped, let it dry and re-harden on the wig head.
The crown of the bonnet can be steamed with a little hand-held steamer to un-wrinkle it.
I hope this helps, and I hope to be able to make a video at some point. Happy bonnet-wearing!