When a bridge is included in geometry, whether 1D or 2D, the geometry preprocessor calculates a set of curves that relate flow rate past the bridge as a function of headwater and tailwater. It is different from modeling the crossing with 2D equations. The water surface ought to be comparable between bridge and no-bridge scenarios, but it likely won’t be the same.
My preference, if the water surface never reaches the lower rung of the bridge, is to model reaches with bridges as open channel. In design of crossings in jurisdictions I work in, the bridge would have to be one or two feet higher than the 100-year flow. Which clearance depends on the scale of the flow. Piers and abutments can be modeled as topography.