Bay Bridge 260K ppl/day + San Mateo Bridge 93K ppl/day is within spitting distance of BART (411K ppl). If there was another whole bridge across the bay (well, maybe two or three) it would alleviate the Bay Bridge and the traffic around it.
Note that I didn't make my point to say that we should build another bridge, just the pedantic detail that BART traffic isn't that much larger than Bay Bridge + San Mateo Bridge, which is a more apt comparison. I think actually you'd want to add in the Golden Gate Bridge, another 110K. So basically, there are more people commuting into SF driving over bridges than taking BART in.