Matera, and the whole of Basilicata/Lucania, is a remote region and always has been.

There are coaches going from Rome to Matera. Flixbus is one option, or Marino (a company I personally don't like, but they've got quite a good share of the north-south bus market). Duration is a not-too-nice 6 hours but it might beat having to fly to Bari and then make your way to Matera.

https://www.flixbus.co.uk/?_sp=54865...f-c5390509448d
https://marinobus.it/?gad=1&gclid=Cj...AaAk0gEALw_wcB