I find that a lot of cotton things, especially bandanas, are too stiff to use when first purchased (I often wear them as ‘do rags.) What’s the best way to soften them up? Wear them a bunch? Put them in every load of laundry? Drag the behind my friends’ Harley?
I don’t have any cotton ones that haven’t been through 15 washings by now. That’s the best way.
My current wife makes my bandannas out of hemp and they start out pretty stiff. When I get a new one I put it into a nalgene bottle full of salt water. Then while I work outside it’s in one of holders on my toolbelt sloshing around. I finish by setting the whole thing out in the sun for a day.
Wring vigorously, wash in next load with fabric softener. Tumble dry. This seems to speed up the process.
Wringing, washing and tumbling dry is the best way to break in most cotton clothing. Unless it’s underwear. In that case, the humane thing to do is to take a trip out west and bring them to “The Shorts Whisperer.”
Fred Astaire said every time he got a new suit, he took it off the hanger and threw it up against the wall a few times. Then he’d wad it up and jump on it. He said you have to show a new suit who’s boss. 
I tried ironing a few new bandanas with a dryer sheet in between them. It had almost no effect. I think it’s in the washing and drying. I think plenty of use in absorbing sweat and snot are sure to help, and that gives you an incentive to wash them. 