Vernazza to Volterra in July on a Sunday

Public trans does not look to good. You may have to rent to car on Saturday in La Spezia where there is an hertz that is listed as 9am to 12 pm on Saturday closed Sunday

Train schedules tend to be cut back less on Sundays than bus schedules, so I would plan to do as much of this trip by train as possible. The train will get you to Pisa, and I believe even to Pontedera, which is closer to Volterra.

At Pontedera you would need to switch to the CPT bus on Line 500. If for some reason you need or want to take a bus rather than the train from Pisa to Pontedera, you'd want CPT bus line 190 out of Pisa.

Links to the CPT bus schedules.

You'll need pick a departure that doesn't have one of the letter-codes underneath the bus numbers; those all refer to restrictions that make the buses unavailable to you for Sunday travel.

As a back-up plan, there are also rail connections that will get you to the Volterra-Saline-Pomarance station that seems to be less than 10 miles from Volterra. You'd need to be prepared with a verified telephone number of a taxi that serves that area and a cell phone, of course.

I took the 190 bus from Pisa to Pontedera to connect to the 500 bus to Volterra. In hindsight, taking the train to Pontedera would have been better. Buses depart from the big square a block from the train station, reached by exiting the square immediately in front of the station at the far left corner.

RE 21187
Dep 10:46 VERNAZZA
Arr 11:05 LA SPEZIA CENTRALE
IC 657
Dep 11:23 LA SPEZIA CENTRALE
Arr 13:24 CECINA
RE 6947
Dep 14:30 CECINA
Arr 15:03 VOLTERRA-SAL.-POMAR.

The bus will arrive inside the walls of Volterra while the train station several miles away. I opted for the bus and was happy with that decision.

But there's only one bus into Volterra on Sunday (from Florence). If you can make that one, you're good! Leave Florence at 15:40, arrive Colle Val d'Elsa at 16:10, change buses and leave there at 16:45, arrive Volterra at 17:35.

Janet, the OP is traveling from the Cinque Terre, not from Florence.

If the OP takes David's suggested trains, s/he would have to wait until 18:45 to get a bus into Volterra from the station. I have no idea whether taxis would be available. Trains from Vernazza to Florence take 2:45 to 3:45 hours. Taking one of those trains and then the bus right into Volterra might be preferable to some of us (Frank and me, I guess!).