If you can take a straight edge and push it past the bearing without making contact and turning it then there is almost no way that your board should dive in. There are only a few logical possibilities.
1. the in feed fence sticks out farther than the out feed does. Check with a good straight edge.
2. you aren't routing the entire profile in the first pass until the bit gets to then end of the cut. As you feed in, the router bits natural tendency is to push the wood away from the fence. (For every action there is an equal and opposite reaction.) Try running the boards through a second time and see if that solves the problem.
3. you are cutting a profile that removes the entire edge leaving nothing registered against the fence that you started out with. Use double sided tape or brads/pins to attach a second board on top of your work piece and let it stay registered against the fence.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.