Working with a "winter white" hat I found on eBay, I matched a near-white chiffon fabric for the band and bow. If you look at her hat in relation to the color of Brad's shirt, you can see it's not quite as white. Trying to find the right shape hat is hard enough.
Create the band by pleating a strip of chiffon on the bias. The bias will adjust to the hat's curve and lay more smoothly around the crown. (More detailed post of this process). Secure it by hand with needle and thread - all the way through the hat. 
I made the bow by cutting two 22" x 4" long strip of chiffon with tapered ends. Bag line and leave a slit on the side to turn right side out and press. The bow is basically folded accordion-style. Starting from the center I folded it every 2-1/2" - the tapered ends left slightly longer. I hand-stitched the back of the folds together and then scrunched the back to give the bow a full effect. You'll have to play around with this to get it how you like. Secure the bow over the hand band to hide it's seam - either with hand stitches or even glue.
The hat rests far back on her head and you'll need to add a hat pin to get the same effect. Her hat also acquires some dimples - presumably from her own hand holding it down as she runs.
