Chuck if you are trying to take a 3/8 bit and start in a 3/8 hole bad things are likely to happen. There is very close to no humanly way possible you can do that without it starting to bounce around as it gets going. You just can't normally control the torque that accurately. The risks are: bent shank on bit, broken bit, bent armature on the router, & totally losing control of the router and having it come out of your hands.You can do as suggested and lean the bit into the cut as you move it but the groove won't likely be that accurate. This is really a job for a plunge. Like Harrysin likes to say, "A plunge router will do anything a fixed base will do but a fixed base won't do everything a plunge will do".
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.