I have used a bandanna in the past but my current pre-filter for my drinking water is a pair of nylon "footie" stockings.
They are packaged in the kind of little plastic container that us kids used to get cheap plastic toys in when we put a quarter in and turned the crank on a vending machine. Total cost of my pre-filter $.59 at Walgreens.
When I used the bandanna the pre-filtering process was agonizingly slow.
BTW I only use fresh nylon "footie" stockings.