You have 2 options starting from Orinda. First, you can take BART into San Francisco then take a Golden Gate Transit bus #72 or 80 to Santa Rosa. Another option would be to take an AC Transit bus #74 from Orinda to Richmond then a Golden Gate Transit bus #40 or 42 to San Rafael then take the Golden Gate Transit #80 north to Santa Rosa. Good luck!
BART wont help you because it does not run through Marin and Sonoma. You can take AC transit and a bus across the Richmond bridge to the San Rafael transit center Then you can take #70 to Santa Rosa.
Golden Gate Transit goes to Santa Rosa.