I have a similar dust problem here. I use a leaf blower for a quick clean, just to remove the 2 inches of dirt, and sand. Then compressed air for the rest, making sure that I blow out the filter also. Then hose it all down with the water hose. Let it dry in the sun, turn off the fuel, then drive it into the barn. It runs out of fuel just about the time I get it parked.
Since it's already mostly clean, then it doesn't take much water, and the whole process takes less time than it took for me to make this post.