Yes it's fine to ride a bike in your first trimester, I rode horses through most of mine and my Dr. okay'd it. Your baby is safe right now behind your pelvic bone, as you get towards the end of your first trimester he/she will move up and that's when you have to start being really careful. As far as the rest of the pregnancy that is up to you. Depending on how comfortable/confident you feel on the bike, you absolutely wouldn't want to fall that is for sure. Congrats on the baby!
-God Bless-