No local rules or regulations that prohibit flying under the Golden Gate Bridge. As a matter of fact, as other people have pointed out, it can be (and often is) the safest way to get from the Bay to the open ocean. The FAA has seen it and never have I heard a peep of complaint from them.
Of course in this post 9/11 world that we live in, there is always the potential that someone will see a Bell 206 and know that Ossama is going to Allah while smacking into Alcatraz.
The only things to worry about are the chances of some idiot decideing that throwing a can or bottle into a rotor system would be fun, or worse, picking that exact moment to end it all! I don't know the exact stats, but when I was doing Bay tours, I remember that the number of jumpers was over 1,000. The way to fly under the bridge is to change course at the last second to hopefully avoid any potential conflicts. Another possible conflict is to look out for the nets that hand under the bridge. They are there as a safety device for the workers that are constantly doing maintenance on the bridge. Hate to have a hammer through the system as well.
On the plus side, it is one of the most spectacular moments most passengers will ever have in a helicopter.