I have been using Quechua three second "pop up" tents for almost a year now, I camp when working away from home and have subjected them to some serious weather with no problems whatsoever, and many put up/pack away cycles without incident, the larger ones are too large for biking but the smaller ones pack to 0.5 Metre diameter and ought to fit somewhere, google "Quechua seconds" ought to find their website, oh and they are cheaper in France.
Stewart