Hammocks and bicycles travel well together...
But what has been mentioned is true: you must have bottom insulation. Notice the quilt hanging from below. You can start with some wal-mart ccf foam, or try this stuff, which is really nice:
http://gossamergear.com/sleeping/1-4-wide.html
There is a bit of a learning curve, and hopefully if you choose to pursue it, you too are rewarded with the comfort and packability that makes hammocking so addictive.