Er, SAAn FrAAn, I think you must be thinking of one of the peninsular bridges, the Dumbarton or San Mateo bridge, not the Bay Bridge.

If you are thinking of that, 101 is just as good, perhaps better than 280.

However, the bridges are probably not any better than going on 880 all the way. Basically, theres bad traffic on all the possible ways.

One possible alternate, if you have a another person with you on the way to OAK so you can take the carpool lane, is to take 237 from Sunnyvale to 880 (also use the carpool lane on Lawrence Expressway to get to 237 if you're coming from Cupertino). Without another person, forget the 237 parking lot.