I rode my bike around the battery then up East Bay towards the bridge. The bike/walking lane is clearly marked and really wide. I thought it was exhilarating to ride across this bridge...it didn't even feel that long or steep! It felt mostly safe because there is a tall metal fence on the edge and you're protected by a ~3ft tall concrete barrier between you and traffic. However, I'm a weenie and got a little freaked out by traffic coming at 60mph towards me when I returned to town.
I highly recommend this experience if you'd like to get some exercise!