Get some good lights, ride defensively and as though people haven't seen you. Then give it a go. I ride on busy roads, but make sure I am safe by taking the lane when required, using a mirror and good lights.
There is danger in everything we do, commuting on a bike for me is no more dangerous than taking the bus (in fact I feel far more safe on my bike!).
The only way to find out if it'll work for you is to try it a few times.