Lawrence Millstein, at present, there are no Bart stations that go into downtown San Jose. There is a Bart station constructed next to the Berryessa Flea Market (Berryessa Station). However, I don't know if this is up and running, as of yet. It was suppose to start in 2019, but now they're saying it will open sometime in 2020. The bus and light rail routes (Berryessa Transit Center), opened a few months ago on December, 28, 2019, and is up and running, to support the Bart once it's open... YOUR BEST BET ON SATURDAY'S is to take the CalTrain at Diridon Station in San Jose to catch the Bart at Millbrae (if that's where you're headed). *Because of the WEEKEND CLOSURE of Services to SF, from Feb, 22 - Mar,29, 2020. If you're trying to get to San Francisco on a Saturday's, you'll have to take the Caltrain and get off at Bayshore. There will be FREE Sam Trans buses available to take you into San Francisco. The first Caltrain for Saturday's leaves at 7:08a, 8:38a, 9:51a etc., etc
You can take Caltrain to Bart 7 days a week, connect at Millbrae Station.
I suggest you check the BART station website for other frequently asked questions and answers
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