Do not store your fur in a bag of any type. Bags (especially plastic) reduce air flow and therefore circulation of moisture, which can speed up the drying out (biodegradation) of your fur. Bags (especially cloth) can also cause wear and broken hairs over time, at the points where it rests against the fur. For the same reason do not try to protect your fur from dust by hanging a piece of cloth over the shoulders.
Use of garment bags is OK for travel and short periods of time when you are specifically trying to protect your fur.