You'll clear immigration (aka Passport Control), collect your bags, clear Customs and recheck your bags in Rome.

I don't agree. You should be able to check your bags from DCA all the way to BRI. Just give the AA agent at DCA your Alitalia flight info.

You'd still need to check-in with Alitalia in Rome (or online in advance if you can), but you should not see your bags until you get to Bari.

So, I should check when i get my boarding passes about what I should expect with my bag when I arrive in Rome?

"I should check when i get my boarding passes about what I should expect with my bag when I arrive in Rome?"

You should be able to check your bag through. If you do check it through, then you go through Immigration (passport control) in Rome, and Customs at Bari. If you don't check it through, you will do both Immigration and Customs at Rome. But definitely ask them to check it through.

(Customs and Immigration are two different things.)

Did you book these tickets separately?

I booked them all at once, not seperate.

I booked them all at once, not seperate.

By separately we mean did you book DCA to FCO and FCO to BRI rather than DCA to BRI. If you didn't book directly with the airline then you may have separate tickets even if you booked it as one itinerary

I suspect the former as normally Alitalia codeshares with Delta and if so it'll probably mean your luggage will be checked to Rome only. It also means that if there is any problems and you miss your flight to BRI you'll have to buy a new return ticket for that leg

Even if the FCO-BRI leg is booked separately, one can still get AA To tag the bags all the way to BRI. May need some persuading, but it can be done.

I'm almost always able to check my bags through even when on separate tix. (except for the discount airlines that don't interline)

I recently had two separate tickets on United for same day flights and they checked my bags to my final destination.

We have flights scheduled next year on Delta and Air France - again two separate tickets (don't ask) and Delta has indicated that they will check them all the way through to our final international destination.

So I also think that even if you have two separate tickets, just ask when you initially check in for your first flight if they will check them all the way through.

Delta and Air France are together in SKYTEAM. Anytime you buy tickets within the codeshare they always check your bags through with no problem.
In Rome, you will get off the flight and head to the "in transit" or connections section instead of going down the escalator to immigration downstairs.