An ELL post says
"Over" doesn't necessarily mean only an arch bridge — any bridge that is substantially above ... "over" whenever the emphasis was on the state of being above/distant from the river
I guess that means the part pointed out by blue square rather than the red.
In other words, in everyday English, the bridge mainly refers to the part on which pedestrians and vehicles pass through.
Is my understanding right?
Note: Parts of bridge piers pointed out by red square are under the water, which we can't see directly in the image.