My boss needed a mobcap, so here's what I figured out. This is not to be worn to a reenactment of any sort - it's just a quick, easy solution to a costume problem.
First, iron your fabric, then draw a circle on it - eighteen inches in diameter. Cut it out with pinking shears.
Now, take some purchased bias tape - single fold - and press it open. The fold lines should still be visible. Pin it to the wrong side of the circle two inches from the outer edge all the way around. Stitch along those fold lines, first one, then the other, leaving a space where the two would meet; you want to be able to thread your elastic or drawstring in there.
For this, I tied a little knot on one end of the cord, put a safety pin through the knot and threaded it through the channel. But after adjusting it on my own head and then tying it to fit, I decided that was too fussy - I redid it with elastic.
I had a very narrow length of elastic and threaded it through with a pin, as above. I didn't even measure the elastic beforehand - could just tell it looked okay when it got a certain ruffled look to it.
This a very basic method, but very simple! And, do you wonder why a library director wants a mobcap?
Well, every year we try to plan a whole summer of fun for the local children, and she and Trisha gear up in costume (related to that year's theme) and travel to the local schools to tell the kids all about it. This year the theme has to do with dreams and nighttime, and they're wearing their pajamas! So, she had the idea that a sleeping cap might be in order. Trisha won't be needing one - she'll be pigtailing her hair.
(You could of course make this larger if you want - for some reason, the eighteen inch size was what I kept finding in my online researches - even Colonial Williamsburg gave that dimension.)