change train at Bologna Centrale station

Which platforms are these two trains likely to be on?

16 (underground) and #3. If they don't change the intended tracks you'll have to Walk up 2 flights of stairs and take the underpass

Hi, Dario, Thank you so much for the information. So I should have just enough time to reach platform 3 if the first train is not delayed. If I failed to reach the platform on time, would I be ok to use the same ticket to get onto next train, and buy a new ticket ON THE TRAIN if needed? Sorry about the additional question, it is my first time in Italy and is anxious about the jurney. Natalie.

Bologna is a large station but it's not gigantic so 25 minutes should be enough if you don't go too slow (walk at a 'normal' pace, have no mobility issues, etc.). Be ready to get off the incoming train as soon as it stops (maybe even get out of your seat and go stand by the door as it's slowing down entering the station). There will be signs in the station listing the track number for your departing train so you should double check that as they sometimes change the track/platform/binario (the Italian for track) number. Just head straight there.

If you do miss the second train you will need to buy a new ticket in the station. The kiosks are easy to use and usually there is an employee around to ask if you can't figure it out, but hit the British flag icon to get the English version. There are 'manned' ticket counters but the lines can be quite long. If you wait till you get on a train without a ticket you'll pay a fine in addition to the ticket price. And since by this point you will have missed the train to Bari anyway why wouldn't you buy a new ticket in the station. But unless your incoming train is late you should be OK.

If you do miss the second train you will need to buy a new ticket in the station.

No, this is partially wrong. If you purchase a through ticket on the official site and you miss a connection because the first Trenitalia train is late you are always protected and you can get a new ticket for free.

If I failed to reach the platform on time, would I be ok to use the same ticket to get onto next train, and buy a new ticket ON THE TRAIN if needed?

There are only reserved seats on Freccia trains, you can't board one without a ticket specific to that train.
and take the first free seat you see. Do it and you'll be fined.

If you get on and walk along the aisles looking for a conductor, You'll be asked to pay Only the administrative fee for on board purchases, but it would be a pia dragging your stuff in tow.

Just get a new ticket at the counters, there is a small booth just in front of the escalators and the girls working there speak some English.

Natalie, one of the things that confuses first time users of Bologna Centrale is that one of the intermediate underground levels is actually an underground parking with the "kiss & ride lane. Try to zoom in the map I linked above, when you see cars you have not arrived out of the station!
It's not an easy station to transfer in 25 minutes, the new underground tracks and services have been squeezed under the old building, but if you wait by the exit doors before the train arrives you should do it.

Larger version of the station plan here: https://www.customwalks.com/images/uploads/blog/Bologna_Centrale_station_map.jpg

Thank you so much to all of you for the detailed advice! I am very grateful.

While the locals understand their train system, as an infrequent user it is important to know your train number. That will always be posted on the board along with the platform number but your destination may not be shown on the board. As stated earlier, regardless of conditions of the ticket purchase, IF you miss the connection because the train is late, you will need to go to the ticket window to a get a new ticket but it will be free.

Thank you Frank! I shall remember your advice.
Natalie