Traffic ticket

Short answer, “yes” you will be able to rent a car.

Not all cities send fines to foreign residents. They of course notify the vehicle owner (the car rental company), and the car rental company provides the name of the driver to the authorities (and charges your credit card an admin fee for doing so). But then it’s up to the city to send the fine to the driver overseas or not. Some cities like Florence do. Others may decide that it is not worth it because only a small percentage of those fines sent overseas get collected.
Since you have not received the official fine from the city of Bologna (with registered mail) you are off the hook. The city has 360 days to send it to you from the time it received notification from the rental car company. It looks like that time has expired, so it means they decided to trash your fine.
In reality you’d be able to rent a car even if you received it and refused to pay.

Does driving in Italy normally result in a traffic ticket, so it seems.

It shouldn’t result necessarily in a ticket, but I don’t understand why so many Americans get caught by the ZTL cameras.
Do people pay attention to road signals when on vacation? Or was the brain checked in at the airport with the luggage?

Does driving in Italy normally result in a traffic ticket, so it
seems.

We drove in Italy- never got a ticket

We drove in Germany and France- got a ticket in both.

YMMV

As stated, there should be no problem renting a car. I didn’t receive a ticket in Sicily, but have received them in Germany, and one in Spain. For one of the Germany ones, the municipality never sent me the actual violation. I paid the other two right away.

Every ticket that I have received except one has been till related. The one exception was me just starting to pull down a one way street going the wrong way and immediately stopping and turning around. This one was in Florence.
I do they they purposely target people who are driving rental cars. Not to mention the rental car companies get a nice chunk of cash for just giving the police our information.

I made a typo on my last reply, I meant to put that most of the tickets were from trouble with the tolls

I do they they purposely target people who are driving rental cars.

How? And why?

The reason I say that is I purposely drive very cautious and mindful in Europe and it seems like every other car is going by me a incredible speeds are recklessly. I don’t speed and I have to be the only car on the road who doesn’t most of the time.

How would the cameras know it was a rental car?

Do you think they take pictures of all the speeding or not-toll-paying cars and throw out all of them except the few rental cars, and then just send tickets to them?

I know they can tell a little bit from the lincense plate numbers. I may be wrong and maybe all of those people I see speeding are getting tickets as well but that seems like a stretch. I haven’t got a traffic ticket in the us in 24 years.

I think the rental cars do have stickers with the codes for the rental agencies on the front windshield. So it is possible that once the Traffic camera takes the photo of the car going through the toll booth it can be identified as a rental because of those stickers.

I know they can tell a little bit from the lincense plate numbers

You know it wrong, they can't.

Those speeding know if the speed trap ahead is working or not, if the speed trap monitors the average speed between two points or if it works like the old ones, when the speed limit is valid only up to the next intersection and so on. In short, you don't know much, but you judge everything.

Getting fined more than once because of tolls... except for the fact that unpaid tolls are not fines, the all story tells more about you than about the rest of the world trying to scam you. Just like making an U turn in a one-way road and expecting not to be fined.

I think the rental cars do have stickers with the codes for the rental agencies on the front windshield.

Not in Italy, but it doesn't matter. Even if they programmed cameras to recognize such stickers on the windshield and not to memorize only the back plate numbers... how could they justify it? And how could they get those codes from rental companies without a lewful reason. And the cops that must check any fine given by a camera, how could they approve only the fines linked to rental cars without breaking the laws?

I guess you are right that these tickets are my fault thanks for the lesson that I’m a terrible driver and evidently it’s only me. Even though I have had a license for 36 years in the us and had one ticket and no car wrecks!

Oh for Pete's sake- the tickets are your fault- you are the driver. By your own admission it was you who drove down a 1 way street in the wrong direction and other tickets were toll related- not really a ticket at all- just a toll violation. Your post indicates you committed multiple toll violations. If you blew thru a toll booth here in US you'd get the same treatment.
Implying that the Italian police are out to get you and every other tourist who drives a rental car is so ridiculous. The fact that you've not had a ticket or accident in US is completely irrelevant.
Count yourself lucky that you never received the actual ticket from Bologna and stop giving new travelers the wrong idea about driving in Italy.

Could not agree with you more Christine, well said

From what I see on this post, I think we've already lost that Christmas cheer.

The fact that one has never received a traffic ticket in the US doesn’t mean much.
In my experience there is a lot of leniency by the highway patrol at least in California.
Most freeways in California have a low speed limit, 65 mph (105 km/h), or at most, outside metropolitan areas, 70mph (113 km/h), yet unless you drive 15 miles (24 km/h) or more above the speed limit, nobody fines you, and there are no speed cameras, only live officers with a radar. Cameras are used only at major intersections with street lights.
ZTLs don’t exist, and tolls are only on bridges and occasional rare “express lanes”.
Bus lanes are also rare, aside from some downtown San Francisco, I’ve never seen any.
Unfortunately Italy (all of Europe actually) has adopted the camera enforcement mechanism and set the camera to snap a picture whenever you go above 5km/h (3mph) over the speed limit. Cameras are ubiquitous and in addition there are the uniquely European pedestrianized areas (ZTL) and bus and taxi only lanes (plenty of them). All of this in addition to the lack of parking in cities that were designed before the age of cars, therefore causing people to collect parking violations too.
The opportunities of incurring into a traffic violations are therefore much greater in Europe than in America. In over 30 years in America I managed to collect only one ticket (didn’t fully stop at a stop sign), while in the previous 13 driving in Italy (mostly in Florence) I collected dozens, and that was even before they installed speed cameras and instituted ZTLs.

The reason I say that is I purposely drive very cautious and mindful in Europe and it seems like every other car is going by me a incredible speeds are recklessly. I don’t speed and I have to be the only car on the road who doesn’t most of the time.

How do you know those other drivers haven't received speeding fines? Did you manage to identify them, track them down and confirm with them several months down the line whether they received a ticket or not? Of course not therefore you can't claim that it's only tourists being targeted.

I've driven within Europe (excluding the UK) for many years, I've received two speeding tickets in Spain. Both occasions were fully justifiable, I was speeding and I got caught. I paid the fine and took it on the chin. I've been caught speeding once in the UK despite regularly exceeding the speed limit. If I want to ensure that I never risk a ticket then all I have to do is stay within the limits. Coming on forums and whining about it isn't the answer, acknowledging and obeying the rules of the country you're visiting is.

As already said, one can still rent a car.
If it happens again you can fight driving fines on: https://bussgeldcheck.bild.de/ no matter which citzienship you have.
But I suggest trying it out only when you assume u have good position to win..

This is a keeper -- a great statement --- " you don't know much, but you judge everything."

There is another difference in the some states if not in all of the US only the driver of the car can be ticketed and not the car itself. For example, in CO with the photo tickets, the driver has to be identified. While in college, my son's car was registered in my name and my address. When he would get a photo ticket for speeding, the ticket with the picture of the driver would come to me. I would make a copy of my driver's license picture, attach it to the violation, with the statement that I was not driving the vehicle at that time. Ticket dismissed.