I have to ask... why bother with a cover?
Just speaking for me, I figure that the bike is weatherproof and any moisture that collects overnight can easily be wiped up with a clean cloth. I carry a small microfiber cloth just for this purpose, but since I always stay in hotels, I just use one of their towels. During the day, I'm usually on the bike so it's not just sitting out in the sun where a cover could be useful.
I have considered carrying a cover, if only to reduce the chance of it being a target for vandalism or theft, but that's probably unlikely and even something as small as a cover would take up valuable storage real estate when I take my longer trips.