BART does not go to San Jose. You can take Amtrak Capitol Corridor from San Jose Diridon Station (has connections to VTA busses and light rail) to Emeryville where you can catch local buses if needed. Or if you get off a bit earlier at the Oakland Coliseum stop, you can connect to BART. The trip on Amtrak is about 1.25 hours and $16 for a single ticket, potentially cheaper with a monthly pass.
There s no BART station in San Jose OR Emeryville. Perhaps you are looking for the Capital Corridor Amtrak train?
nearest is Fremont, it takes one hour to MacArthur BART, then free shuttle to Emeryville
I thought San Jose doesnt have BART.