I am going to be another bay area native to say - practically impossible unfortunately - but may be doable if you are willing to do a bit of bicycle riding, and have spare time.
We have a decent train line that comes down the peninsula (caltrain), but connecting busses are slim, take too long (you would be looking at a 2 hour one way journey). The train ride one way is about 45 mins.
I think your best bet would be to take Caltrain down the Peninsula to Menlo Park or Palo Alto stations, then ride a bicycle.
Portola Valley Training center is 3.5 miles from the caltrain stations, and has a dressage trainer (mostly a hunter jumper facility these days).
Seven Oaks dressage http://www.sevenoaksfarm.com/ Is just beyond the training center (so again, a 3.5 - 4 mile one way bike ride)
Glenoaks has a dressage trainer as well http://www.glenoaksequestrian.com/trainers.htm and is a bit further down the road, a little over 5 miles from the train station.
Edited to add!
Almost forgot about Stanford! The “Red Barn” is just two miles away from the Palo Alto Caltrain station. Rachel Williamson is a good dressage trainer that works out of the Red Barn… but not sure if outside riders have access to lesson horses in her program. They DO have lesson horses for the general public (NICE horses), but I am not sure if they have dressage specific lessons in that program.