it IS possible to visit Chianti wineries by bus from Florence
Ciao wanderer,
You might be able to visit all of the wineries you've selected by BUS but most definitely not all of them in one day.
Most wineries are located off the main roads in the hills - you might be able to get near an estate and then have to do a bit of walking to arrive at the estates.
The most limiting factor is the bus schedules - you might get to where you want, but then not make it back in time to catch the next bus (when there is one).
The easiest to visit by bus would be Verrazzano and Vicchiomaggio starting in Florence. They are both located just off the SS222 road that connects Florence to Siena and passes through the heart of Chianti. SITA buses do go down this road often, most of them arriving to Panzano in Chianti.
You can see bus schedule from Florence into Chianti here:
http://www.acvbus.it/orari/365.pdf
The ones with a cross are the ones that run on Sundays, the ones with a hammer run Monday through Saturday and the ones with an A within a circle run only Monday through Fridays. As you can see, most arrive to Panzano, and only a few make it to Radda, Castellina or Gaiole.
The
Castello di Vicchiomaggio is the closest to Florence, from the SMN train station, catch a SITA bus toward GREVE IN CHIANTI and get off at the LE BOLLE stop which is about 2 km from the castle - from here it is about 20 min uphill walk up to the castle where tastings are offered. The basic tastings are offered every day and don't require reservations but if you want a tour or lunch included, better to book ahead:
http://www.vicchiomaggio.it/eng/services.html
The
Castello di Verrazzano is just a little bit further down the same road with a wine shop right off the road where you can do wine tastings right there without booking ahead of time. You get off on the next stop after Vicchiomaggio which is called GRETI. The estate itself is located 2 km up the hill beyond the wine shop so if you want to visit the winery and tour the cellars, you'd have to do the climb up. For tours, you should book ahead - see details here:
http://www.verrazzano.com/en/programmes-wine-tours/ ("Vendita diretta" refers to the wine shop).
If you want to do tours of the cellars, make sure to contact them and book, telling them you are arriving by bus and I am sure they'll suggest which are the ones you should take. Depending on how long each tour and tasting takes, you might still be able to do both before heading back to Florence.
If you do just tastings you might have time to reach Greve - it is a charming town and there are more shops here where you can do more tastings

.
The
Castello di Brolio is in Gaiole in Chianti which is further away. There seems to be only one bus from Florence in the afternoon (departs 1.35pm and arrives at 3.30pm) and only one from Gaiole in the morning toward Florence (departs 6.55am and arrives at 8.55am in Florence). So you can get there but getting back might be a problem.
It is easier to reach Gaiole by bus from Siena since there are more buses - the 127 line from the train station has departures at 7.05am, 12.50pm, 2.15pm and 5.50pm.
You can also reach Gaiole by train, sort of. Take the train Firenze-Montevarchi (schedules on
www.trenitalia.com/). Be sure to be in Montevarchi around 1.00pm to take the bus for Gaiole leaving at 1.35pm.
I was going to suggest taking advantage of a special promotion offered by the Florence province of a tour in Chianti with wine tasting included but it is only offered on Thursdays. It seems you cannot consider it but others might find it interesting so here is the link:-
http://www.firenzeturismo.it/en/events/100-promozioni-speciali/365-visite-guidate-nel-chianti.html - It seems like an interesting proposal so I might be doing it myself soon and then tell you all how it goes.
My conclusion: from Florence, visit by bus both Vicchiomaggio and Verrazzano and if time permits, Greve and then return to Florence. You can spend the night in Florence again and head off to Siena in the morning.
If you want to do more, you should rent a car. If you rent, make sure to eat something with your tastings and do more spitting than drinking.... or the driver doesn't drink. Don't get behind the wheel if you feel you cannot drive safely - the SS222 road is a 2 lane road, winding up and down lots of hills.
If parking in Siena concerns you, know that there are several lots around the historical center. The most convenient one where you always find space is the one at the train station. From here, hop on the bus that takes you up into the historical center. But if you don't feel like driving at all, you can do a day in Chianti by bus and the second day in Siena (get there by train or SITA bus from Florence).
EDITED 10/2013: The Chianti wine tasting tour offered by the Florence tourism board on Thursdays is NO LONGER OFFERED.