Sorry I didn't see this sooner, but for future readers, I am a regular between Monterey County and the Bay Area. Not as frequent these days, but still know it like the back of my hand.
The
Monterey - Salinas Transit agency runs buses once or twice per day to/from San Jose Diridon or San Jose Airport, Bus 55 to/from Monterey and Bus 86 to/from Salinas. Fares are $12 adult / $6 disabled, senior or student. Day passes are the same cost, so be sure to get the Day Pass for any MST buses you may take before or after your long distance ride.
55 schedule to/from San Jose Diridon Station:
https://mst.org/wp-content/media/55.pdf
86 schedule to/from San Jose Airport and San Jose Diridon Station:
https://mst.org/wp-content/media/86.pdf
Another option is the
Amtrak bus between Salinas and San Jose Diridon Station. By policy, you must book a train segment with any of the Amtrak buses. I usually book the multi-segment ticket as SNS-SJC bus + SJC-SCC (Santa Clara) train and throw away the train segment. Like airline tickets, book the train segment as the second segment so the entire ticket isn't cancelled for no-showing. This Amtrak journey is usually around $20-$25 one way.
Once you hop off either bus at Diridon, you can catch Caltrain up to San Francisco and points between, and vice versa for the reverse journey. Or catch the VTA Bus 181 to/from Fremont BART to get to/from the east side of the Bay.