Buses between Siena and Colle Val d’Elsa are part of the Siena regional lines (Siena Mobilita) while buses between Colle Val d’Elsa and Volterra are part of the Pisa regional lines (CPT Pisa). I purchased tickets before boarding the buses, but my recollection is that I purchased them separately. Buying the second ticket was no big deal as the news stand right beside the bus stop in Colle Val d’Elsa sells tickets for both bus systems.
I did a quick check on the rome2rio website and then confirmed the Colle Val d’Elsa to Volterra portion of the information on the CPT Pisa website. For June 16, it shows a very early connection departing Siena at 6:20 and arriving in Volterra at 7:50 and a midmorning connection departing at 8:40 and arriving 10:35. Last bus back is at 17:20. I’d suggest you start your research with the rome2rio website, which has links to the regional bus line websites if needed. If you go to the bus line websites, you’ll need to look at the extraurbana lines. The rome2rio website has been favorably mentioned many times on this board but yesterday was the first time I actually used it. I found it to be very user-friendly.
I strongly recommend that you reconsider taking the train to Poggibonsi and then doubling back to Colle Val d’Elsa. The bus between Siena and Colle Val d’Elsa takes about a half hour, which is about the time it would take you to get to Poggibonsi on the train. Then you’d need to go to the bus station and take a bus to Colle Val d’Elsa to connect to the same CPT Pisa bus (#770) as had you taken the direct bus from Siena. Going via Poggibonsi, while doable, would just make the longish trip even longer and more expensive. Plus, it won’t allow you to get to Volterra any earlier or leave any later.