You could model the culvert/bridge as cross-sections with lids. If the water surface will never touch the low chord, then you could just ignore the culvert/bridge and just use cross-sections making sure to take into account roughness changes.
As for culvert entrance losses, the manual provides different values based on different types of configurations. In reality, you should try and calibrate the losses based on actual flow data, but this does not happen often as there is usually no data.
It is up to the modeler to decide if what they see in HEC-RAS is too much entrance loss or not and adjust as needed. This could be done by checking culvert losses in HY-8, culvert nomographs, hand calculations, or other software.