I would definitley recommend staying in Domenico's place! It was spotlessly clean for me and the interior design is very impressive. Bitonto is a pleasant small suburban town about half an hour's train ride away from Bari. The public transport i.e. the train is so so handy and not expensive. I found that the last train was usually around 10pm from Bari back to Bitonto.
Domenico makes a massive effort with providing vouchers for a local cafe (definitely use these), a fully stocked fridge of drinks, and various dry crackers and jams. The room itself is quite cave-like so that aren't any windows. It's located very close to a Spar supermarket, and the train station is less than 10 minutes away by walking.
Great place to stay as a solo female traveller. I felt very safe and also felt like I could contact Domenico if I had any issues. She was super communicative, even when she was on her own summer holidays.
Definitely would recommend staying here! :)