There aren't that many buses that make stops in Tavarnelle on Saturdays - you'll have to wait until 18:05 (there's another one at 18:35, it's the last for the day).
You need to get off in Tavarnelle and then walk to Poderi in Chianti. Since it is 2.5km outside of town, it should take about 30 minutes. If you're arriving with luggage, maybe you can have them go pick you up in Tavarnelle?
How are you planning to move around during your stay?
You can use that schedule for local towns in between Poggibonsi and Florence.
The only other line in town is line 372, also heads back to Florence.
You can see the general schedules for the Chianti area here: http://www.acvbus.it/index.php?SEZ=9
first thing is to look at the days it runs at the top of each column:
SAB = saturday
FESTIVO = Sunday
LUN-VEN = Monday-Friday
then head down to where you want to go and read across... if there is no time, it means it doesn't make a stop there.
If you'll depend on public transport, you'll need to first get to another town that offers more options - either Poggibonsi (for Siena or SG) or Florence (for Pisa, Lucca and most of Tuscany). Most of the small towns in Chianti are not easy to reach, as all buses first go back to Florence!