Dear Jojo
Welcome to slowtrav ... and to italy!! Strikes are a matter of daily life.
Yes, there will most likely be a strike until 9pm on the 11th of feb. You could try to take a train just after that. OR you can try to get on one of the "guaranteed" trains. The eurostar that runs on the main line, which includes the rome-florence route, usually runs despite strikes, but is very crowded. Other people on this board can explain better than I.
Your options are two. One, you can go to the train station, stand in line at the ticket or information counter, and hope that someone will find you a spot on a train that is running. But be ready to face crowds.
Your second option, good especially if you are staying in italy for a week or longer, is to stay at a B+B in rome for your first night, and leave for florence on the 12th. There are lots of suggestions for hotels/ B+B's in rome on this board, just use the search feature or check reviews or classifieds. Nicholas Inn is a contributor here and i hear it is fine. Contact where you're staying in florence and just tell them you're coming the next day because of the strike. I'm sure you won't be penalized.
You can change your train ticket before it leaves with no penalty, or you can change it after the fact, and you lose only your reservation fee which is about 8 euro. To change ticket, go to ticket window at train station. They speak some english.
Don't try to take a bus to florence!! The train takes 1h35m. To drive, it takes 4 hours. I can't imagine a bus.