Caterina and Giulia have a very nice apartment just a few blocks from the old city. The location is great—plenty of cafes, restaurants, and shops within walking distance. Bari Centrale train station is an easy 10 minute walk.
The loft is cozy, with a couch and a table for relaxing and dining. The refrigerator is full size, and there are enough kitchen items for cooking and eating at home if you wish. Also, the host provided snacks, coffee, milk, and a package of pasta and can of pomodoro sauce, which was a thoughtful touch!
Check in was painless: I buzzed an adjacent apartment and the owners let me in and showed me the place.
There are a few issues. It was very cold in April, and there were no obvious heating elements. The internet was slow to the point of being unusable. The apartment has been divided into two rental units, and you can hear vibration of walking and music/talking from the adjacent unit, often quite loud.