I'd cover it wet - it's bound to drip dry some. Please tell me you are using a real MC cover and not a tarp. They are built to vent. Just leave some kind of air gap at the bottom. When its through raining - then let it air off. It won't take long. Keep it waxed - wax keeps the water running off!
03 Suzuki GSF1200S Bandit, HIR headlights, GIVI shield, SWMoto guards, Hayabusa shock, lowered 2", H/S backrest & tailrack, Avon Storms, VStrom Hand Guards, IBA SS 1k