Good question.
I would think that there would be a database of the bridges and their clearance heights posted so those companies moving big machinery could consult it.
I made my living for a while hauling oversized loads. A dispatcher would contact, in my case, ODOT. ODOT would ok the load, but the driver had to follow the specified routes. Heaven forbid if he went off route. OH yeah, different states had different rules to follow for the same load.
There was a major foulup here. I wonder if those involved could read English.