The connection from Rome to Siena is one of the most simple and comfortable throughout the transport network departing from the capital.
I did back and forth for two years because of the University and I have always found it very well.
Train would required a change at Chiusi and then take a bus to reach the center of Siena - the bus is to be comfortable and always punctual.
The bus departs from bus Tiburtina Train Station, ticket costs 20 euros each way, to be bought at the Bus Station.
The company that takes care of transportation is the Sena, Inter coach, all relevant information is available on the site http://www.sena.it
The bus leaves from Tiburtina Rome, takes three hours to get to Piazza Gramsci, which is a few minutes away from Piazza del Campo and the historical centre of the City of Siena.
The bus stops at: Bettolle (exit A1), Rapolano, Siena Viale Toselli, Siena Stazione FS Porta Camollia Siena, Piazza Gramsci Siena, Siena S. Colonna Marco, Monteriggioni, Colle Val d'Elsa, Poggibonsi.
Schedules are subject to change, even if I never had big problems, and part a coach more or less every two hours.
Also on the site of the Sena is the opportunity to purchase tickets online without going through the ticket office. If you buy in advance, you may find special offers ( or bids) on the ticket special rate of 5 euros.
If you dont want to spend a night away from Rome, your visit to Siena can be done back and forth, spending a beautiful day in the heart of the Val di Chiana.