If you're an American, Brit, Australian, Canadian, or otherwise don't speak, read, write good Italian, trying to find good information that is easy to use and understand for public transportation on Pantelleria may be a real problem for you. It was for me. Only after I was on the island was I able to get good information, and then because a vineyard I wanted to visit sent me the appropriate links, which cleared everything up that I had not been able to find satisfactorily while home in the USA.
As I was staying along the harbor, I had easy access to the local bus. I did not feel I needed a car. The bus would take me wherever I wanted to go and for those times when I wanted to get off the beaten path, and go further than the bus went, I hired a guide for roughly 5 to 6 hours for less than the price of a day's car rental at the airport.
The Marsala Travel Bus company is based in Marsala but the link to the site as I've posted for this attraction is the link that will take you to the information for Pantelleria.
There is a very good map of the routes the bus runs on the site. Here, however, for convenience, is the link to the map: http://www.marsalatravelbus.it/images/cartina-isola-trasporti_1.jpg. With that in hand, you may have a sense if you're renting a dammusi that is not nearby the bus route that you want a rental car; however, if you're nearby the bus route and staying in a dammusi, you may want merely rely on the bus if there's a stop close enough to your liking to which to walk.
However, to see the scheduled times and stops for the bus, you first link to this site: http://www.marsalatravelbus.it/, then you scroll down to the "READ MORE" button. Once you click on the "READ MORE" button, you are on the page where you can either download the schedules in a PDF format, or, you can scroll a little further down the page, past the PDF links, and the schedules are on the page, just in a different viewing format than if you download the PDF.
Your hotel or a local can instruct you where to catch the bus. The maximum fare I paid one way was 1.30 euro.
One thing to know: your driver will not be calling out the stops, at least mine did not. You will drive right by stops if no one has asked to get off at a particular location.
Now, the problem is that the stops are at times just a tiny little blue sign and you really don't know you're coming up to it, or, if you've passed it up. So, don't be thinking that after you've boarded you just need count the number of stops you must pass to get off where you want get off as you may have passed some stops beforehand and had no idea you passed them up. Take my word for this from the voice of experience!
When you get on the bus, I suggest you have written on a piece of paper the stop where you want to be let off and hand that to the driver and let him know that's the stop at which you want to be let off. A handy thing would be to have a printout of the schedule, and then highlight in yellow or circle with a pen or pencil, the stop you want to be let off at and if you give that to the driver, he'll know what you want.
The only reason I don't rate the bus service as 5 stars is the fact that it is indeed a challenge to know where you are on the route without stops being called out in advance. Even when the bus does stop at a given location to let someone off or to let someone on, the drivers do not say outloud the name of the stop.
The main stop (Capolinea Pantelleria) in the town of Pantelleria is just off the Piazza Cavour, in front of the post office on Via Edmondo de Amicis. You'll see the blue bus stop sign and also you'll see the designated parking for the bus with "BUS" in yellow on the road as well. This is one of the few instances when you can't miss the stop!