Most of the bridges across San Francisco Bay are limited access. A car free friend in Marin County said that when he had to get to the east side of the Bay (and back) he would call the agency running the bridges and say when he would need to cross. Usually withing half an hour of the time he got there one of the emergency service trucks that constantly shuttle across across the bridges would give him a lift over. Now there are bike racks on most buses running over the bridges. As others say contact the state agencies on both sides of the bridge. I expect the police would just say no. Greyhound might do it for a price. Adventure cyclings Yellow Pages has contact numbers for each state government. That alone was worth the price of joining for me.