One bike? If I had to keep it outdoors it would be a very inexpensive bike. Under a cover it's likely to keep a lot of the mornings high humidity underneath and next to the bike. Though between leaving it uncovered in the rain and crud that's going to fall from other things and putting it under a tarp, I guess I'd opt for the tarp.
How bout a big locker like they use on the docks of marinas for each boat owner to store the excess stuff. Some are tall and about phone booth size and you could hang the bike in it. Usually the boat lockers I've seen are well ventilated. But they also looks somewhat home made too. So maybe the better ones are DIY.
Are you certain you can't keep it inside? I have two in my dining room that never gets used for dining. Are you sure you don't have room inside?