I always had problems with my sons stroller getting dirty in the trunk of my car or the back of our truck. I noticed one day that we had a few folding lawn chairs that come in their own storage/carry bags. I got the biggest bag from one of our chairs (that had a footrest attached) and slid the closed stroller in it. All but the front wheels and the handle fit inside. I could also pull the drawstring to tighten around the stroller.
Now whenever we pull the stroller out, the seat part is always clean and dry. It was also easier to carry over your shoulder when not in use by using the strap attached to the bag.