Rome Airport

Which Terminal should I go to?
There are four Terminals at Leonardo da Vinci airport: T1, T2, T3 and T5 (the last of which is dedicated exclusively to United States and Israeli carriers). The Terminals for departures and arrivals of national and international flights may vary depending on the destinations and the carrier, which you may contact for specific information.

How can I reach the Terminals?
A free shuttle bus service is in operation year round, connecting the terminals, car parks and Cargo city, every 15 minutes on average (from 1 a.m. to 4 a.m., the shuttle bus must be called from the intercoms installed at the stops).

http://www.adr.it/web/aeroporti-di-roma-en-/pax-fco-fiumicino

You most likely will arrive at Terminal three and depart from three. Since it is separate tickets I hope you have allow enough time to make the connection - at least three hours, maybe four. You claim you bags, go through immigration/passport control - plan on at least an hour and maybe two depending on a bunch of factors, customs is walk through the green door, from there check-in for Alitalia. If you don't or cannot check-in on line, then you need to make sure you are checked in 45 mins prior to departure. Then you will go through security again and finally board the plane.

You will arrive at T3.
All Alitalia flights to Bari depart from Terminal 1 - Boarding area B.
Google the Fiumicino airport map to get an idea of the location. It's not that far to walk actually.

One of the terminals at FCO is closed due to a fire this past spring. check with you airline to see what terminal you will be coming in on and the do the same with Alitalia (you can do that by doing a flight status check for your flight number on a current day, the terminal/gates don't change that much from day to day).

As you have separate tickets and checked baggage, I'd agree with Roberto. You will arrive in T3, go through immigration, then pick up your checked luggage, clear customs, take the elevator/escalator up to the main level. Exit out the front doors of T3 and turn left, walking on the sidewalk in front of T3, T2 and down to T1 (perhaps 650 meters?). There you will find the correct Alitalia counter, re-check your bags, go through security, and then head for your gate.

Because you are going from T3 to T1, you're walking against the one-way traffic flow.... so it's faster to walk rather than loop around the airport on a shuttle bus. The fire in May has caused substantial damage and repairs have been proceeding poorly. There is a great deal of unrest among many of the employees working in what they feel are improper conditions - so it's a stressful environment. Well, more stressful than usual at FCO.

I hope you gave yourself at least 2.5 to 3+ hours to make this transition. Good Luck!

Thanks so much. This was the exact information I needed. We arrive at 930 a.m. and don't leave for Bari until 230pm, so I think we should be fine.

Good plan.

That is a crazy routing. Arrive T-3. It would have been faster to get off in Rome and take the train.

Trustinsoul.
I found it odd that you would fly to FCO, then to AMS, then back down to VCE. It would have made more sense to fly to AMS then to VCE with KLM. Or fly to FCO then directly to VCE with Alitalia. Both KLM and Alitalia are Delta partners with the Sky Team alliance.

If you are departing from FCO to AMS with either Alitalia or KLM the departure terminal is T1.
Delta arrives at T3. So the situation is similar to the poster's above.

Please forgive earlier post - having a bad brain day -
Am Not arriving in FCO - am routing Atlanta-Amsterdam-Venice.
My departure is FCO-JFK-Atlanta
Sorry for the confusion - headed to lunch, maybe that will help the old gray matter!