Many central valley cities have closed their bus terminals, but Stockton's remains busy enough. There is a break in the mid-day between 12 and 3pm, but mornings and evenings are fairly busy. The station patrons are not the jet set, but Greyhound appears to have worked hard to clean up its image by getting rid of the bums and winos hanging around. I saw nothing unpleasant in the group that climbed aboard my bus. I took an Express bus from Stockton to LA. The bus left at 9:30am and arrived in LA at 4pm, which is not a bad experience given that normally I'd be quite tired by the drive. The bus was nearly full, but I lucky enough to sit next to a pretty 19 year old black woman, and we shared some interesting conversations. My fair was paid by my employer, but to get a significant savings over even the cheapest airfare, pay for the ticket at least 7 days in advance.
The bus system in Stockton is regular but slow. You're better off renting a car or getting a ride from someone. The bicycle path along the Calaveras river is a quick short ride for the experienced cyclist.