Sounds like a bridge I was riding until just recently. Single lane each way, no shoulder or sidewalk, guardrail beneath my center of gravity, over an interstate. Can you say zero margin of error? It was definitely the scariest part of my ride, especially at night.

Here's the way I dealt with it. First, in all cases, take as much of the lane as you feel you need to. The traffic will just have to wait behind you, or pull around you if they can. Analyze the traffic ahead and behind you as you approach. (If you don't have a rear-view mirror, get one.) If possible, try to time it so that there won't be cars in both lanes at the same time that you are on it. That way, either you have no cars in your lane and you're fine, or there are no cars in the other lane so that those in yours have plenty of room to pass. If this is not possible, stick your hand out and carefully and gradually merge into the center of the lane as best you can so you don't get squeezed to the side. There have been 2 or 3 times (in 2-1/2 years) that I have actually had to stop and let some traffic pass before mounting the bridge, so don't feel like you can't do that if you must, although obviously it is nice to not have to.

I don't know what the surrounding landscape is like for your bridge, but on mine, in one direction I had a long straight-away so I had plenty of time to plan, and in the other, I had just come off of a right-hand turn where I always took the lane, so I was right there anyway. And the traffic was never constant bumper-to-bumper, more like groups of cars that waxed and waned with the light cycles. If your situation is different, you may need to experiment with other strategies.

Hope this helps. Good luck!