Unbleached flour has a more natural taste because it has not been tainted with the chemicals used to process bleached flour. Millers treat their bleached product with chemicals for more than one reason. The most obvious is cosmetic. Bleaching agents whiten the flour, but just as important, millers cut their costs with chemical processing. Flour must be aged to strengthen its gluten content, and natural aging of unbleached flour requires keeping the product in a warehouse for several months. Flour processors discovered that they could avoid that storage expense by using chemicals to age the flour artificially.
When you purchase unbleached flour, look for an established brand, which is your assurance that the flour has been sufficiently aged.