score:1
As my experience shows, you will pass through immigration in Rome but customs check will be done in Bologna. At least how it was when we were doing similar itinerary to Catania - our bags were checked at Catania Fontanarossa before handing them to us.
So I think that either there will be no explicit customs check, or it will be done in airport of final arrival.
I remember we had another flight to Milan via Zurich, and there were no customs check at all, we just grabbed our bag off carousel and were free to go as Zurich-Milan was domestic.
Update: I also think they will put you on a next flight to Bologna if you miss your designated one for the reason of customs delay, and I think Rome-Bologna flights are fairly frequent so you won't be delayed too much.
Update 2: This assumes you have a single ticket booking. If you have two tickets that are completely separate, you will likely need to pass immigration, then get your bags via customs and resubmit them at check-in in Rome. There is a big chance that you will miss your second, non-connected flight since immigration in Rome took an hour waiting in lines last time I've been there. In this case you should consider changing your tickets.