Time to make connecting flight to Bari from Rome on ITA airlines

Are you doing carry-on-only luggage, or checking baggage?

Are you coming from outside of the EU when you land in Rome?
Is Bari your final destination?
Finally, are your flights to Rome and to Bari on the same ticket with the same airline?

Sorry to say, there is a good chance, depending on the factors previously asked, that you
will miss your flight. Apart from normal congestion, how fast you can get off the originating
flight, and how much, if any, of a mess there is related to EES implementation (if you are
coming from the US) are large factors.

If, as noted, your flights are on the same ticket, then you are at least protected to be placed
on a later flight with no additional charge. If, though, your flights are on 2 separate tickets,
be prepared to push, shove, and run.

If you have checked bags, they should be transferred and you will not have to pick them
up and recheck. But you would want to make sure at origination that they are tagged
correctly.

You will do customs in Bari but that will probably just involve walking through the green channel, unless you have goods to declare.

Immigration you will do in Rome. If you are coming from outside the Schengen Area, that is.

I have the same time for a connection in Rome, on ITA, this week. I will let you know how it goes!!

If you miss it, there are flights to Bari later the same day, I'm sure.