Ciao Jan,
Love the idea of staying in Pienza and then hiking all the way around the area! On your day to Bagno Vignoni, make sure to stop in San Quirico as well, it is small and charming -- and you get great views of traditional Tuscan landscapes (including the tiny chapel Vitaleta on top of a hill) on the way between Pienza and San Quirico.
Just make sure:
- take the white roads, not the main asphalt roads -- there are too many cars and NO space for walkers along the main roads. You'll have to certainly take them for some stretches of road, but overall, get a local map and take the unpaved roads that connect the farmhouses in the area.
- what time of the year are you planning this?? there is NO TREE COVER in this area, so you want to head out early in the day and walk back in the early evenings, making sure to park source of light in case you are caught still on the road once sun goes down. The white roads generally don't have any lighting in any way. We've hiked between Pienza and San Quirico in early April and the temps were perfect, we will needed hats to protect us from the sun.
As far as a driver from Siena down to Pienza, take a look at these drivers and contact them for price estimates. Arrange travel back to Siena on your last day as part of the package, too!
http://www.tuscanytotravel.com/ (operates out of Florence)
http://www.autonoleggioilgirasole.it/index.en.php (operate out of Cortona so more local)
http://www.get-tours.it/tours/pienza (Cortona based too)
http://www.autonoleggiosenese.com/excursions.htm (based on Siena)
http://www.sartinisiena.com/rental_with_chauffeur.php (based in Siena)
Consider if you're interested in making stops along the way, it will be considered more of an excursion/tour as opposed to a transfer from one point to the next without stops in the middle. It might influence cost, so make sure to indicate clearly in your request what you want to do!