Firenze to Volterra / and points Tuscany

Private transportation to those places would be quite expensive. Either you'd have to pay the driver to wait while you visited the town, or you'd have to pay the round-trip fare.

I'm 99% certain that you can find bus tours (or perhaps smaller van tours) to those towns. Conceivably you might find one tour that goes to both places, because you would go right past San Gimignano on the way to Volterra. Try Googling bus tour Volterra. I'm guessing there are so many tours that you probably will not need to book far in advance. It's true that you will probably need to make the arrangements at least one day ahead of time, but you should have a good idea of the weather and what you want to do a day or two before the tour, right?

There is public-bus service to both Volterra and San Gimignano, but it is very slow, and most travelers wouldn't have enough patience to go that way.

Some of us do have that patience and have visited both Volterra and San Gimignano by public bus. If you have the time, it's easy and cheap to do.

Edited to add: Not sure whether you're asking about day trips or about going to the next place to spend the night, which is what we did. I would agree that trying to make day trips to those towns by public transportation will be too time-consuming. If you're traveling to spend the night, you might also look at MyDayTrip.com.

I've done both day-trips by public bus, but I am an odd tourist, indeed.

the bus will take about 2:30. I believe there's one leaving around 8am and a return around 8pm. Giving you around 10 hours in Volterra.
I'll check to see if I can find the timetable.