Parking in Matera, Italy

I stayed on that street as well (is it Torretta ai Sassi?)--but caveat, my two trips were prior to 2020, and I know it's gotten more popular (though I do think September should be okay). We always parked on Via Lucana and did not have any trouble (sometimes in the small surface lot and sometimes in street spaces--we had a small SUV one of the visits). When you search the address on Google Maps, you can click on "nearby" and enter "parking" to see the options. The small surface lot comes up as "Matera/public parking space"). I think that area is a bit less hectic.
Our B&B provided directions so I would check with them first.

We stayed in the Sassi in October 2021 and it wasn't easy finding parking in the town. The lot recommended was always full. We found street parking

I'm not sure if it's helpful, but this is the information my hotel sent us before our stay last year. We opted for the hotel shuttle, but that parking garage (Nicoletti) is open to anyone and seemed to me to be a very good spot.
but, at 35 euro per night, it's probably among the most expensive options. There is info about free parking art the end. (We stayed, on this repeat visit, at the SEXTANTIO CIVITA, a remarkable hotel, but with very expensive pricing; we booked pretty late and only the highest priced rooms were available).

<<<The hotel is located in the heart of the oldest part of Matera the Sassi. This is a restricted traffic area, PLEASE DO NOT DRIVE TO THE HOTEL, IF YOU DO, YOU WILL GET A FINE. Below few suggestions for parking:

SECURE GARAGE WITH SHUTTLE SERVICE:

-PARCHEGGIO NICOLETTI - WELCOME MATERA- WELCOME MATERA (40°39'58.2"N 16°36'14.2"E) –
CAR SPOT RESERVATION NOT REQUIRED there are always places available for Sextantio guests, so please enter even if the board at the entrance says full. The garage shuttle service will be available to take you to the hotel. The reservation of the shuttle for the departure day is required.
Address: "PARCHEGGIO NICOLETTI" Via Vincenzo Cappelluti, 1 - 75100 MATERA, (900 meters far from the hotel)
Rates: € 35 per night including 2 transfers to/from the hotel. Any extra transfer during the stay has a cost of €10 each way. Payment at the hotel.
Notes: Dogs admitted on the shuttle only with pet carrier. Alternatively, the garage is 14 minutes walking,
Opening time: every day, 7 am – 11 pm.

OTHER OPTIONS:
- Multi-storey car park “PARKING VIA SARAGAT”. Fare € 1,00 per hour.
From there a public shuttle “Linea Sassi” is available every 30 minutes. You can buy a ticket on board and stop at “Madonna delle Virtù”. Sextantio Le Grotte della Civita is 100 meters ahead, on the staircase on your right. Alternatively, you can call us if you need help to call a taxi.

• Possibility to park in the free stalls with white stripes located on roads outside the restricted traffic area of the historic center. We suggest: Via Santo Stefano; Via Piave; Via Pentasuglia; Via Gattini.

This street is on the opposite side from the sassi--it's nothing like the scrum for parking in the sassi where the larger hotels are located. You may very well have to look for parking at times, but I really don't think it will be that dire. Do ask your b&b as they will have the best advice for the time of year. There is a garage on this side of town, but the b&b will best know if it is for visitors, etc.
When you arrive to town and return from day trips, just make sure you enter the town on the correct route (I believe it is near the hospital if memory serves)--that way you basically just ride up one long street and avoid a lot of aggravation!

Thank you everyone! Avoiding a fine is key!! I've been thinking of going to Parcheggio Sant'Isidoro garage. We'll have a bit of a walk but we've walked with bags and stairs in Italy before.