I've done both, Pressure and Washing. My wife would never let me use our Washing Machine so I used a commercial one at a laundrymat. It worked really well on the canvas cover. My current cover is more of a synthetic material with cloth on the inside. That too was washed last spring and I just hung it outside to dry. I've had no issues with either but I probably wouldn't wash them more than once a year. I would think sun light and the wind at road speed is the worst for wear on the covers.
By the way, you're going to get some dirty looks when you take that thing in to the laundry mat. Best to wait for late evening or early morning when the "hens" aren't around!