pompeii/salerno to matera??

Try Rome2rio.com., Salerno to Matera. They will show you different options such as bus and train. Looks like you’ll have to transfer at least once. Might be easiest to take a train part way then transfer to a bus.

From the Pompeii sight, you can walk (fairly flat, about 25 minutes) or take a taxi to the Pompei train station a mile or so away (note difference in spelling between sight and town). The train that runs near the Pompeii sight is the Circumvesuviana, but Trenitalia regional trains run from the Pompei train station to Salerno. The Freccialink buses are designed to link between select towns not serviced by Freccia trains, and Salerno to Matera is one of those links. You should be able to purchase the Freccialink bus ticket separately (I've talked to people that have done so), but evidently not online. Try purchasing it at a ticket window or ticket kiosk in Italy.

There have been some past posts about the Salerno-Matera bus. You might do a search (see box at top of page) and then send people who have taken the bus a Private Message asking where they bought their tickets.

We took the train from Salerno to Ferrandina which is the closest TrenItalia station to Matera. Pre-booked a taxi which was 25 euros; train for 2 was maybe 9. Pre-booking is key as the station is tiny and in middle of nowhere so no taxi stand.

There is Bari-Matera service operated by http://ferrovieappulolucane.it/en/lines/lines/.

In 2016, we used Miccolis bus to go from Salerno to Matera. We purchased our tickets online from their website.
http://www.miccolis-spa.it. At some point, not to far from Matera, we changed from the bus to a van for the last leg of the journey.