A hammock is a great idea. I was going to suggest a tarp, that's what I've been using. I just use a $3 tarp from the hardware store, some thin nylon rope $5, 4 tent stakes $2, and then a sleeping pad and bag. The tarp, rope, and stakes weigh in at about 1 pound and take up no room really. I can fit them all into my sleeping bag stuff sack. Obviously this wouldn't work well in the dead of winter but I'm not much interested in bike touring that time of the year.
Andrew