I think the major ports (APM, Norfolk, Navy, and the shipyards) are all accessible over tunnels rather than under bridges. For sure, if the Jordan, High Rise, Berkeley bridges, and/or a handful of railroad bridges went down, that would cause problems for some businesses. Take a look at the satellite image of Norfolk/Portsmouth/Hampton. You can see most of the stuff is on the “right side”of any bridges.
Now, how a tunnel collapse would affect the area is a murkier question. Technically, ships could presumably still cross, but I’m sure there would be some kind of disruption. Probably shorter than the time needed to remove a collapsed bridge.
TL;DR: there would be an impact, but I don’t think any bridge serves as a “gateway” to the ports or shipyards.