Filters are used to achieve something. There's no "night" filter that photogs slap on because they're taking a shot at night. There's no "bridge at night" filter either.
A polarizer's main job is to cut down reflections that the photographer would not want ruining their composition. If you want to shoot through a window without seeing the reflections in that window, that would be a good place to use one. If you want to shoot a photo of fish under the water, and don't want the reflection of the sky and clouds and sun on the water, that would be a good place to use one. If you want to take a photo of a classic car and that shiny wax job is reflecting a lot of light like a mirror and you'd like to cut through that to see the paint job, that would be a good place to use one.
Now, what reflections do you expect to encounter from the GG bridge at night that would require a polarizer to cut through them?
Having shot that bridge at all hours of the day and night and from pretty much every angle, I'm going to say: None.
But let's say you want the bridge to be MORE orange than the International Orange it already is. You COULD put a sunset filter over the lens. Or maybe for some reason, you'd like the water to show up more blue, even though it's going to be pretty dark to begin with at night. You COULD put a graduated blue filter over the lens where the water shows through to achieve that. Or maybe you'd like the lights on the bridge to show a star pattern. You COULD put a star pattern filter over the lens to achieve that look. Or maybe you want just the top of the bridge to show up as a sort of magenta color. You COULD put a graduated magenta filter in front of the lens so that the magenta color is at the top and colors the top of the bridge for you. Or maybe you'd like the bridge and it's reflection to be about the same brightness. Normally, the reflection will be less bright. You COULD put a graduated neutral density filter over the top half of the lens to cut down the light intensity of the bridge itself, while leaving the reflection as bright as normal.
The POINT is that you have to decide BEFORE you shoot: WHAT is it you want to achieve with your photo? What do you want it to look like? THEN you can decide if you want or need some sort of filter to help you make that happen.
Here's a photo I shot from Baker Beach with a whole bunch of filters in front of the lens in order to achieve a particular look:
Here's another I shot with no filters on the camera at all, preferring to color filter it later in post processing:
I would say, start by just getting out there, setting up on your tripod, and shoot. Don't worry or even think about filters until you see what you get without them. Establish your base shots that way. Then, if you think you need filters to achieve a particular effect that goes beyond your base shots, go for it.
ETA: By the way, unless you're shooting with film, that UV filter is worthless to you.
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