Pretty sure it's illegal.
It is now. There's no specific rule saying you can't fly under a bridge, but there is an FAA rule saying that you can't fly below 500 feet except over open water, and even then you must keep at least 500' of distance from "person, vessel, vehicle, or structure." Given the congestion of the SF area, you're probably also going to be limited to a minimum altitude of "an altitude of 1,000 feet above the highest obstacle within a horizontal radius of 2,000 feet of the aircraft."
There might also be restrictions due to the presence of airports, heliports, etc. And, formerly, when there were military bases in the area, and Alcatraz was a prison, there might have been further flight restrictions.
That said, the rules for helicopters are apparently different. See here:
Also, way back when, the rules were different:
http://articles.sfgate.com/2005-11-03/business/17401004_1_clippers-treasure-island-global-flightAnd, just to show you that even the pros don't mind breaking the rules when they're flying a simulator: