For those that don't know the OP is talking about lightweight cots... not an old army folding cot. Basically thin nylon held up by some plastic legs and aluminum tent pole sections.
I used a friends one time and found them to be comfortable, but you do need at least a foam pad on them to insulate you from the air moving under you. And I would think the poles are generally to long to find an easy place to carry them on a bike
::Edit:: looks like the thermarest's cot poles do come apart