You can get to Torrita di Siena with train from Rome to Chiusi and from there catch a bus - take a look at this map with schedule for a Sunday (I just mapped for this coming up Sunday): https://goo.gl/maps/zGNYy83Mhm32
the shortest travel time is to leave from Roma Termini at 10.30am (travel time is 2 hr and 20 min) - you can map other times and dates in and see other options you have.
This is better than the other possibilities, which all take you to Florence and therefore take more like 4 hours to get to Torrita......
BUT ---- have you considered how you're going to move around once you're at this villa?
It is likely NOT in the center of Torrita di Siena (I wasn't able to find its precise location online), so how will you get there from Torrita di Siena? Have you received info on its precise address?
Consider renting a car either out of Chiusi or even Rome and driving to your villa, so that you then have your own means of transport to go around the beautiful area you will be in (near Montepulciano and the Val d'Orcia).