Wots wrong with old tee shirts? Especially the kids ones as they grow out of them make ideal dusters and free!
Failing that go asda. Twin pack 2white tee shirts 3quid wear them a while when grubby turn them inside out to dust with. I hav found blue towels can leave marks and fibres particullarly over white grout...With the trade being quite at the mo save pennies where you can more so on thow away items like dusters!...Happy days