Capitol Corridor (California Amtrak) has long run a bus connecting either Emeryville/Oakland or San Jose with Santa Barbara. There are several runs a day. One is overnight.

It's no Lark, but the Amtrak buses are generally a small notch better than ordinary Greyhound. Probably Megabus class. Connects with Cap Corridor trains at the north end and Surfliner in Santa Barbara or SLO.

It's not fast, either; total running time from Oakland to LA isn't any faster than the Starlight. Competitive with Greyhound time. If you want to do the trip faster, ride the San Joaquin to Bakersfield with the bus connection to LA. The last train south of the day reaches Bakersfield about midnight, and the bus gets to LA at about 2 AM (continues on to San Diego arriving around 6 AM). Return leaves LA around 2 AM, connecting with a train in Bakersfield around 5 AM, and arrives in Oakland around 10 AM.

Interestingly, the San Joaquin run with the bus actually is quicker than the best times on Greyhound or Megabus. Still can't beat Southwest or driving, of course.