Train to Rome

You might check your rental agency's locator map first to see if they have an office on the outskirts (well outside ztl).

How about dropping it off in Bari, then take a leisurely train to Rome from there?

Drop at the airport, even if it wasn't simple you won't die and there are two train lines to Rome.

For sure it will be easier than driving inside Bari, searching for a drop point out of the ZTL and walking to the station with suitcases in tow.

Edit: There is a direct train Departing from Bari at 8:53 and taking 3 h and 32 mm. Driving in downtown Bari around 8 AM should be feasible. Maybe the "leisure" option suggested by SJ is better than mine, as long as the drop point is somehow close to Bari Centrale station.

Thanks Dario. I did not know about the train from Bari...everything I looked at was around 6 hrs from Bari to Rome. What particular train route is it?

I have no idea, It's just a Trenitalia FrecciaArgento train departing from Bari Centrale at 8:53 AM.

On trenitalia.com you can click the small grey " i " next to the train code to open a pop-up window with all the intermediate stops. I guess you can point those stops on Google Maps to see where a train runs through.

Or fly, very inexpensive when we flew Rome to Bari to Rome.

I thought you were looking for somewhere in Rome's outskirts.
In Bari, there are several agencies a couple blocks from central train station, not a difficult walk if you have carry-on amounts of luggage. It's not a difficult to the highway from there.

Looks like a 4 hour direct Frecciargento train, Bari to Roma Termini.