I agree with the previous poster that the
Eurostar train is the fastest way to get from Rome to Florence, but I personally think that the slower trains are better not only because they are cheaper but because you will get a better experience overall.
I would discourage you from using the bus to get to either Florence, Rome or anywhere else in Italy (horrible experience with backpackers). The main reason I prefer the train is that Italy is best travelled by the train as train connections are pretty good and regular.