But a plastic bag isn't quite the way to go, either. The reason? Moisture. If your bag is even slightly damp, that dampness will simply stay inside the plastic garbage sack. That can lead to mildew, which will either destroy the bag or render it so smelly that you'll not want to use it again.
So, get something that's got lots of volume, but that also breathes. A cotton pillowcase, if pretty big, will work. Anything made of mesh will also do. It's possible to buy storage sacks from a variety of outdoor retailers. Campmor and REI both sell fabric or mesh storage bags for about $10.
The last step is to find a place that's as dry and temperature-regulated as possible. I hang my sleeping bag in the crawlspace under the house, which is very dry and stays about 60 degrees just about year-around. Do that, while also keeping your bag reasonably clean, and it should last for years.