Can you get a Sita bus at Piazzale dei Martiri di Montemaggio in San Gimignano, to Florence?
Directly the answer is no. You would have to change buses in Poggibonsi.
This was on the sita site http://www.sitabus.it/en/florence-san-gimignano/ and it has links to the schedules.
I found this elsewhere that SITA is now The BusItalia Nord. So you can check their website but it's in italian.
You can however do San G to Siena Directly with no bus changes.