Yes, that bus goes from Manciano to Pitigliano. It leaves Manciano at 1340 (1:40 PM) and arrives in Pitigliano at 1410 (2:10 PM). The "Feriale" at the top means workdays only (definitely not Sunday, and not holidays--ask locally about those). The "SC" means schooldays only (not Saturday, I assume, but verify). I don't remember when your trip is scheduled, but if it might fall within the local schools' summer vacation period, you need to verify that the bus will actually be running then.
Bus fares aren't usually shown on timetables, and I don't know how much you'll pay, but in the whole scheme of your vacation, it won't amount to much. It's possible a round-trip ticket would save money if you're doing a day-trip. I took a couple of short bus trips in the Orvieto area that cost me 4.40 euros per round-trip, or about $5 each.
Has anyone given you the pronunciation of the two towns you're interested in? They are roughly:
Mahn CHAH no (H's are silent, as in "aah")
Pee tee LYAH no (H is silent)
There will probably be a "SORANO" sign on the bus; it might be a placard sitting on the dashboard. The intermediate stop at Pitigliano might or might not be mentioned. I always check with the driver to be sure I'm no the right bus. If you don't want to attempt the pronunciation, write out your destination in all capital letters and show it to the driver if you don't already have a ticket that shows the name of the town.