if you take the bus from Siena to Rome, it will take you three hours. Once you arrive at the bus station, you'll have to reach the places you want to see ... Rome is a big town and it will not be easy/fast to move from one monument or museum to the other! There are so many things to see - 1 day is probably not enough! Personally I think that, staying in Siena, it is better to make day trips to the wonderful Chianti-area, to the Val d'Orcia area, to Florence, to Lucca ...
It is definitely all possible however, I agree with Pro Loco Sovicille that while in Tuscany concentrate on all the many things there are to see here. If you need to catch a flight out of Italy to go home, then try and do it from Rome so you can go in a day early and spend the entire day there, sleep over night and then use the train to catch your flight out.
If you want to make the most out a trip to Rome you could check out an organized tour which would organize your time for you and make sure you see all the major sites.