I wash all my covers, including my Proraps, with my diapers. I store the dirty covers in a bag next to my pail, since I found that putting them in the pail with the dirty diapers made them smell a bit. When I wash diapers, I just throw the dirty covers in with them. I do hang the covers to dry rather than putting them in the dryer. My covers have held up very well doing this.
I also don't wash my covers after a change. If the cover seems wet inside, I let it air out until the next change. If it doesn't feel wet, then I just use it again.