Yeah I bought a shemagh from the Amazon link you posted. I don't blame you at all. They are pretty highly rated overall. If I had read more of the reviews I would have known the dye bleed was a potential issue. It seems like it's only certain colors that have that issue. :/
I just ordered some machine-washable bandanas (https://www.amazon.com/gp/product/B01ETYZ20U/ref=oh_aui_detailpage_o00_s01?ie=UTF8&psc=1) and Buff-like scarf knock-offs (https://www.amazon.com/gp/product/B01J1AMQWY/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1).
Also if anyone is looking for dust eye protectors, I found these for a couple bucks: https://www.amazon.com/gp/product/B004CLJSDI/ref=oh_aui_detailpage_o00_s01?ie=UTF8&psc=1