Should be plenty of traffic on the bay.
I used to live in San Jose, and could easily pick up the traffic reports from the USCG Vessel Traffic System:
USCG has transmitters/receivers on several mountain tops
https://www.navcen.uscg.gov/images/marcomms/cgcomms/Rescue21/SecSanFran.jpg
You should hear them easily with the stock antenna and probably inside your home. An antenna outside your home and mounted up as high as you can reasonably get it will allow you to hear the ship/boaters better. Almost all VHF Marine traffic is simplex, so there won't be high level repeaters to listen to. With simplex, it'll work as well as your antenna lets it. If you have some altitude above the bay, you shouldn't have a problem. If you are down on the flatlands, you'll really want an antenna mounted at or above roofline.
You should load in the following channels at minimum:
Channel 16 - 156.800 (Distress and Calling)
Channel 09 - 156.450 (Commercial/Non-Commercial calling)
Channel 12 - 156.600 Offshore VTS (you probably will not be able to hear vessels from outside the gate, but you'll hear USCG answering them)
Channel 14 - 156.700 Inshore VTS (Inside the bay, with a good antenna you should be able to hear most traffic on the bay)
All the VHF channel/frequencies are listed here:
U.S. VHF Channel Information
Ideally, load them all in, with the exception of the two AIS channels at the bottom of the page, and scan them.