There isn't much extra-urban service out of Siena that goes much south of approximately Chiusi.

http://www.sienamobilita.it/mappe/Mappa_EXT.pdf

I found one bus per day each direction between Pitigliano and Siena on ramamobilita.it, but it would seem to be for people living in Pitigliano and wanting to go to Siena for business or shopping, etc.

http://www.ramamobilita.it/~linee_orari/orari/pdf/Q_46.pdf

There is also service between Grosseto and Pitigliano on Rama.

http://www.ramamobilita.it/spip.php?rubrique63

Even if you need to overnight in Pitigliano (at the hotel Guastini), DO GO THERE. Pitigliano is quite unique, quite remarkable and quite unforgettable, especially when gazing at the illuminated skyline at night from the window of the Hotel Guastini. There is no other town in Italy quite like Pitigliano: it's half-way between Civita di Bagnoregio and Orvieto. The direct RAMA bus between Siena and Pitigliano might work.

Here is my review of the Hotel Guastini in Trip Advisor:

"I spent one night at the Hotel Guastini in Pitigliano in mid-May (2012), in a single room with a breathtaking panorama of the skyline of the historic part of Pitigliano. While the room itself was small (suitable for only one adult), it was quite adequate for a short stay, and the views of the Town more than made up for any negligible shortcomings. Overlooking the deep ravine, the room was extremely quiet at night (and is preferable to rooms overlooking the square, which may suffer from some noise during busy weekends of the year). The Hotel has been modernized (new doors, bathroom fixtures, beds), while the large breakfast room preserves the charm of the 1950s, also with breathtaking views of Pitigliano. Breakfast is a simple affair with some very rich selections of homemade ricotta cheese and jams, as well as the customary croissants, bread, cereals and cold cuts. It is the only hotel in Pitigliano proper (there are a couple of small B&Bs), and is very conveniently located about 150 meters from the bus stop (RAMA buses to Albinia, Grosseto (onward connections to Florence) and Valentano (onward connections to Viterbo)). The Hotel also has an excellent restaurant by the same name (and management). Family owned for generations, service is extremely cordial and staff are very helpful. Pitigliano is a gem of a destination, and although quite small and limited in its attractions, nevertheless manages to leave a lasting impression of the visitor. It is most certainly not to be missed, and the Hotel Guastini is an excellent choice for lodging. Allow several hours to visit Pitigliano. Visits to nearby Sorano and Sovana will require a second night (unless the visitor has a car). Visitors intending only to see Pitigliano do not need a car. The RAMA bus service from Florence/Grosseto is quite adequate.
Room Tip: Ask for a room overlooking the ravine, away from the square/street."

QUOTE: "There is no other town in Italy quite like Pitigliano: it's half-way between Civita di Bagnoregio and Orvieto."

NOT IN TERMS OF GEOGRAPHIC LOCATION, but in terms of size!