This would be a tough picture to take because the shutter has to be open long enough to show the bridge at night. But with it open that long, the lights, as you say, would over-expose.
If you had a basement full of cash, you could bribe an official to turn the lights off, then a fraction of a second before the shutter closes, turn them on. This would give the bridge the correct exposure, along with the lights.
If you don't have a basement full of cash, the trick could be done with Photoshop or some application like it. You'd have to use a tripod, or place the camera on some other solid foundation, so it wouldn't move over the space of two exposures.
One exposure would be long to capture the bridge. The second would be short to capture the lights properly. The hard part would be to use Photoshop to erase everything in the short exposure
but the lights, and erase
only the lights in the long exposure, then paste the picture containing the lights from the short exposure onto the long-exposure picture.
I've done that sort of thing way back in the stone age, in a darkroom using film, paper and developer, but it took forever and was only black and white. Compared to that, Photoshop would be a walk in the park.
All the same, better you than me.
