Ciao Alice,
The site linked to above by Doug is the best one for bus schedules in the Siena/SG area, even if it is only in Italian I think it is pretty easy to understand. I think you already found it, given you have names of the stops...
You plug in Firenze - San Gimignano and the time, it will tell you which stations are the ones you arrive at (generally Poggibonsi FS which stands for train station), how long you have to wait and the next bus to take. SG P.S. Giovanni will be your stop ;-)
The same site tells you how long is each "solution", from 80 minutes to 120 minutes (depends on waiting time in Poggibonsi).
Now I don't remember the main piazza in SG, which is round and surrounded by the road, whether there was a bus stop on each side for different directions... so it is likely that all buses might have the same spot, no matter the direction they are traveling.
But like mentioned above, trying to do them both in one day with public transport means watching the time and not spending enough time in each. This spring and summer we've been rediscovering SG and realizing there is a lot to see, and Siena itself requires at least a whole day (we always love staying there so generally take a whole weekend).
So if at all possible, do separate them into 2 days!
In SG, you HAVE to go into the Duomo and see the beautiful frescoes inside, then go into the Palazzo Comunale which has a small painting gallery (pinacoteca) with beautiful masterpieces as well as frescoes (in the main halls) AND includes the climb up Torre Grossa, the tallest of the remaining towers in SG. You'll enjoy a stupendous view of SG and the countryside around.
All of this you have to do, as well as just walk the entire town.... make your way up to see the remains of the old fortress, too!
So all this takes at least 4-5 hours, especially since I'd recommend enjoying lunch and a gelato there (the winner of the best gelato in the world competition is in SG in Pza della Cisterna, the gelateria with Torre Grossa behind it and not the one on the corner).
Bus from Siena to Florence is still a better choice than train, since the bus station is closer to the center than the train station AND requires no transfer while the train does. So bus is FASTER too!