The highway that burned and collapsed in Oakland early Sunday, April 29th is sure to cause massive traffic tie-ups on the various approaches to the Bay Bridge. The section that fell is a critical connector between I-80 and I-580, and the different detour routes are going to be unusually clogged for a while.
Be sure to check local traffic reports (511.org is a good one, but not always the most accurate. They're a little slow to respond sometimes, but they can at least tell you about conditions as of 10-15 mins prior to when you check) before you take a day trip or complete a longer journey in San Francisco. Hopefully, CalTrans will find a workable temporary solution to the problem soon.