You should be able to ride throughout your pregnancy without trouble if you are cautious. I just had a baby 6 weeks ago and my doctor ENCOURAGED cycling the entire time. However, I did have to change my training. I could not do more than 45 miles because the baby truly took a lot of energy from me. It's important, very important to stay well hydrated and drink gatorade BEFORE you ride. Pregnant women tend to be extra dehydrated, so make sure you are getting enough water. You'll also need more calories to sustain your workout. Getting your heart rate up isn't a problem according to more recent studies. However, you do need to listen to your body. If you start to get cramps, slow down to 10 mph if you have to. If you feel weak, take a break. The key is to not push yourself. I was able to run and ride my bike up until 3 days before I delivered. Staying active helped tremendously with labor and delivery. And I was able to start working out just 2 weeks later because I healed to fast.
Good luck!