The Bay Bridge Tunnel has a van service that will take you and your bike across for a fee. You just have to arrange an appointment to do it. When I went through there I didn't know exactly what day I'd be there, and you have to call like 2 weeks in advance or so, so what I did is just roll up as close to the bridge as possible, and stick my thumb out with a ten spot in hand. Took about 5 minutes the fiest time and 30 minutes the second time before someone in a pickup stopped for me.