The reason I asked earlier about the Bascule bridge, is that it's the most common way of lifting an end pivoted bridge in the proto world. If you counter balance the bridge, it will take a miniscule amount of effort to raise it. Lowering it will also be easily controlled. Think of it like a see-saw or teeter-totter. Give it a few grams of positive down force and you will be able to raise and lower it with a tiny motor.
Even a model airplane servo.
The pulley idea won't work unless it located away from the pivot point of the bridge.
Extend the plane of the bridge past the pivot and add weight until the bridge is slightly down heavy.