As a for what it is worth:

I have done a large amount of 3 season hiking with a Eureka Zeus 1 and 2, and have found them to be phenomenal dirt cheap single wall tents. The 2 still seems to be available, but the 1 may be discontinued. I have used it from March to November in the northeast, and never had an issue with pouring rain or freezing temperatures. Also, with me being 6'3.5", it is one of the few families of tents that are long enough for me and my 30 lb dog to spend a night in comfortably.

I have never bike camped, and am just looking at starting it. I looked at tarps, but am really having trouble seeing the advantage over the stuff I already have.