I had heard that one existed, but I can't seem to find it online. I'll be near Chinatown, but I can take BART to anywhere in the city to catch a bus. A cheap train would also work.
[So tempted to answer this with, "let me know when and I'll pick you up," but that doesn't answer the question for Googlers down the line, does it?]
If you're looking for public transportation in the greater San Francisco Bay area, the place to start is always 511.org. A little looking around there will lead you to the Golden Gate Transit site, where you can find a map of their service area.
On that map, draw a vertical line down between Sonoma and St. Helena, and a horizontal line between Novato and Petaluma. The area from the top left corner down to where your two lines meet is Sonoma County.
- San Francisco (Folsom & 7th)
- Main & Folsom (Temporary Transbay Terminal)
- San Francisco (Mission & 1st)
- SF Civic Center (McAllister & Polk)
The next thing you'll have to figure out is where you want to go: the city of Sonoma, Sonoma Valley, or Sonoma County? For the first two, you'll have to get off (probably in Petaluma) and transfer to a local bus.
Depending on what it is you want to do in Wine Country, I'd recommend staying on all the way through Santa Rosa—just north of there is where things really get beautiful, in my thoroughly biased opinion.