My ex-BF, who is both a cyclist and a doctor, did ride when recovering from a cold or flu. Never when the symptoms peaked, but during recovery. He just took it VERY slow and easy, usually 15-30 minutes, just to keep the muscles loose and the blood flowing, never enough to get himself tired. He also topped off with extra amounts of fluids.
He also didn't push it the moment he started feeling better. He kept it going slow for awhile and gradually built his strength back up.
Hope you are feeling better soon.
J
P.S. You also might want to check with your PCP about iron supplements.