You then have to get to Siena as there is no direct service to Radda. Siena can be reached from Florence either by train or bus. Train takes about 1 hour 30 and the bus about 1 hour 15. The bus services leave from outside the station (on the other side of the square). Then you have to take the Tiemme bus #125 to Radda.
If this works for you I could provide more details of times.
Once you get to Radda, how do you plan to move about? it isn't easily reached by bus or train, I highly recommend a car rental to move around once you're also in the area.
In that case, you might consider renting from Rome or Florence to make your life simpler.
Lourdes - good link but where is it and others like it located on the site?
Also, I thoroughly agree with you about hiring a car especially if one is based in one of the smaller towns. Apart from the convenience and not being tied to timetables, one of the greatest things of travelling through the Tuscan countryside is the discovery of an unexpected but charming town or hamlet, or alternatively a view which you can stop and enjoy.