i feel safe wearing my jewelries on public transportation...i do believe if you are to get rob on the bus (not bart/caltrain), they will grab things that they can grab easily and run away. IE your phone while you're talking on it.
However, I do tend to turn my diamond ring around if i need to walk home from the bart station and it's dark out.
In San Fransico, there are some dangerous areas. A friend of mine was talking on his phone. There were some guys grabbing his iPhone from him while he was on the phone. My friend let go of his phone because he did not want to fight with three robbers. Yes, there are some areas in San Francisco that you need to be very careful. You can always cover up by wearing a coat and gloves. San Francisco is cold most of the time anyhow.
The two times I took bart, I thought nothing of wearing jewelry. I was traveling with an elderly friend- she reached over and turned my rings around and used her scarf to cover my LV bag. Made me laugh at the time, but looking back now, I guess she was just being smart.