The American College of OB/GYN in their Committee Opinion on Exericise doesn't specifically mention bicycling. They do state that those exercise activities with a high risk of falling or abdominal trauma (for instance downhill skiing and ice hockey) should be avoided during pregnancy.

Of course there are some conditions that contraindicate aerobic exercise in pregnancy: hemodynamically significant heart disease, multiple gestation, preterm labor during the current pregnancy, preeclampsia, etc.

The primary concern specific to trauma in the pregnant patient is placental abruption. This is a condition in which the placenta separates from the uterus prior to delivery. It may cause, bleeding, pain, contractions, and in the worst cases shock. Abruption of the placenta may also occur in a setting of even minor trauma. At the U. of Michigan all traumas occuring after 20 weeks of gestation are monitored for at least 4 hours. If there is any concern about contractions, etc., the monitoring may be extended to 24 hrs.

In my opinon, noncompetitive biking over relatively smooth terrain is a reasonable exercise up to 20 weeks for those women who do not have contraindications. Increased caution should be observed beyond 20 weeks of gestation. And given the change in center of gravity and resultant awkwardness, it may be prudent to switch to walking or stationary bicycling in the last 13 to 20 weeks of pregnancy.