Miranda - can't answer your fashion question.
BUT yesterday while riding the levee, I saw a lady on a road bike (there are all classes of riders on the levee) wearing a straw brimmed ballcap thing, under her bike helmet. I imagine it's to keep the sun out of her eyes, but my helmet came with a little visor, and riding a road bike, my head is down enough that I don't get sun in my eyes. Besides that's what the spiffy biker-shades are for.
Straw hat under the helmet looked really silly.