Transbay Tube is a underwater tunnel used by Bay Area Rapid Transit trains between San Francisco and Oakland. It is the only other crossing besides the Bay Bridge between San Francisco and Oakland. It is also the highest ridership segment on the BART system.
However the BART system does not normally operate 24 hours a day. 24 hour service may be offered in the event of a planned Bay Bridge shutdown.
During the overnight hours when there's no BART service, AC Transit Route 800 provides link between Downtown SF and Oakland via the Bay Bridge. Other AC Transit routes provide transbay service during daytime hours.
San Francisco Bay Ferry provides ferry service between several East Bay locations (Oakland, Alameda, Richmond) and San Francisco mostly during weekday peak hours.
While a dedicated bus bridge (substitute bus service) is provided in the event of a planned tube shutdown, such as to accommodate weekend construction, it is not generally not possible for unplanned shutdowns.