ACV bus company has a direct bus Florence Greve in Chianti.
The terminus in Florence is in via Santa Caterina da Siena 15, in the SITA bus station (about hundred meters from the railway station of Santa Maria Novella).
Florence Greve in Chianti bus takes about 1 hour and costs about 3€
To download pdf bus schedule, see the page Florence – Gaiole in Chianti (direct bus 365).
Versione italiana: Firenze – Greve in Chianti