Stick with a bandana. You can find large/oversize ones in hiking stores, or online.
The one linked is a fleecy-type material. I had originally thought you were talking about what we used to call a drive-on rag; simply an army issue triangular bandage which, when completely unfolded, covered your fave VERY well. To keep the dust out (rarely worked that well, but, hey, you look pretty intimidating with that & tinted dust goggles).