A lot will depend on when you are traveling, however, I see there is a bus (370A) that runs between Barberino and Florence with no changeovers, it will take you into the city center, and it only takes about an hour.
If you are traveling on a weekend or a holiday, it most probably will not have the most convenient of hours but it will still be do-able. Always be sure to double check the hours, they vary from week days to holidays & Sundays. Saturdays are normally not considered a holiday even though they are in the weekend. BUT if the Saturday is a national holiday then it will have special hours. If you are looking to do a round trip - be sure you know the last return time for the public transport, otherwise it could be quite costly (either a night in the city or a taxi)
If you are looking at renting a car or getting a driver (NCC - driver with car, this is not a taxi and normally they can give you better rates), then I would suggest that you do this so to see the scenery - like organizing a mini-tour, which could be a great way to enjoy the travels, the scenery and maybe a vineyard or two.