I was about to mention Tarptents (www.tarptent.com) if you haven't chosen yet. I don't know why the above poster had problems with it, but I've hiked with two people who used them, helped set them up and take them down, and slept in them, and I'd say they're the best option. You can get a two-person tent for not much more than than the weight of a lot of one-person tents, they're quite easy to set up, quite stable (point the front door into the wind and use panniers/bags to create a wind barrier for the lower part that's not protected by the beak, and you'll be quite comfy) and have plenty of room inside. They're meant to be used with trekking poles, so for biking you need to take along one or two extra poles for the front, but those don't weigh much more at all. You can get a one person tent for even lighter, but at that weight I'd take a two-person model just for the extra room.

If you really just need shelter for one person and will be in places with trees, I'd say you owe it to yourself to try a hammock. I have a 60 dollar hammock with bugnet attached (Grand Trunk Skeeter Beeter) that's lightyears ahead of sleeping on the ground in terms of comfort, and all you need is a tarp to hang over it (covers your bike as well) and you're set.