Here's an easy and inexpensive way to make a bonnet. Start with a cheap cloche hat. It can be made from felt, straw, fabric, woven, etc. All you needs is something with a relatively stiff and narrow brim. You will also need single fold bias tape (preferably 7/8 inch wide with a wider gap between the folds), ribbon for chin straps, and decorations. I used a stiff crocheted hat from Daiso Japan.
Next you will need to cut off 1/4-1/3 of the hat. Start with a slit that extends to almost the center of the hat. Don't cut too much off at once, you can always cut out more later if necessary. After you cut a portion out put it on your head like a bonnet and see if you need to cut out more.
Next use bias tape to bind the unfinished edge you just cut. It's much easier to use a glue gun than sewing, as most hat-making materials are difficult to sew. Make sure you fold in the ends of the bias tape.
Finally, add chin straps to the pointy end of the brim and trim with any trimming you want. Most of my trimmings are in boxes right now, so I just decorated with a wide ribbon. I will add more trimmings when I get a change to unbox all my stuff.