Around here, nearly every USFS campground we go to is a "Pack It In, Pack It OUT" area. There is NO garbage pickup. The people in the nearest towns usually don't want campers filling their dumpsters, either, so our garbage goes home with us.
We have a plastic trash container that fits under the sink, lined with a plastic bag. We also have plastic bags that we use to pick up the "presents" left behind by our dog.
We tie the bags tightly, and store them in the dump valve compartment until we get home. During a three or four day trip, we might generate one or two bags of trash. It simply isn't a major problem.