If you decided not to hire a car, you can go from Rome to Siena by bus (2h45min, 15-24€) or train (3-4h, 16-37€). We recomend the bus as it is direct (by train you need to do some transfers), it takes more or less the same time, has a similar cost and arrives in the historic center of Siena (the train leaves you a little outside).
Baltour group buses (Baltour, Eurolines and Sena) depart from Rome Tiburtina station, which can be easily accessed by Metro Line B (direction Rebibbia, fourth stop after Termini, the bus station is across the street). The bus will leave at Piazza Gramsci, in the historic center of Siena, from where you can easily walk to your hotel (if you go without a car, rather than choosing the Smart Choice hotel, is better to choose one of the options that are in the same center). There are about 9 buses running every day from 06.30.
Although not essential, it is advisable to book tickets online. On this page you can also find the bus schedules. If you don't reserve online, arrive early enough to secure a place.