i hike and climb a lot in the north cascades and have successfully, though not always, used the tarptent rainbow. light, big enough for two people, and super fast to set up. it's bug proof and generally pleasant (lots of leg and head room). only once did i not like it when we had 40mph gusts and rain. it does not have much lateral support, but i'm not sure you'll be in mountain-like kinds of storms while biking across the country:
http://www.tarptent.com/they have other good ones as well, some that are more storm-worthy solo shelters.