Staying at Trastevere Romanesque Apt" was simply the best experience me or my friends ever had with Airbnb (actually with any b&b).
Francesco went to great length to make us feel truly at home, welcoming us really late when we were almost 3 hours late compared to the initial planned time, presenting us a fridge completely full of stuff which helped us for much more than just what it was supposed to (breakfast), spending a lot of time to explain to us what to visit, what to do, what are the "good tricks" only locals knows, even being completely sick and exhausted.
Moreover the apartment is really nice, there are lots of little things which shows an "eye" for the details, especially aesthetic details :).
I am normally much more in favor of options like Couchsurfing, but if I come back with my friends to Roma, I will definitely try to stay again at Francesco apartment :)