is it easy to go from fiumicino to tiburtina by train?

All of the tickets on the Leonardo Express are considered 1st class and the train is nonstop. The trains to Tiburtina are regional trains, they make several stops along the way, so they take a longer.

There really are only two trains from the airport, the Leonardo Express, and the FL1 Regional train.

The Leonardo Express goes non-stop to Termini, cost 14 euro, takes a little over a half hour, and then you would need to find another train on to Tiburtina.

The FL1 makes a number of stops, terminating at Tiburtina in just under an hour, costing just under 10 euro.

While the FL1 is a bit slower, you have no changes to manage at Termini, so it would be my choice.

costing just under 10 euro.

8 EUR to be exact.

Very easy. Take the FL1 not the Leonardo Express.
The FL1 is a regional train going, I believe, to Orte.
The station before Tiburtina is called Roma Tuscolana, so when the train stops there get ready to disembark at the next stop about 5+ minutes later.

reading the fine print carefully on the trainline app.

Why not book on the actual train company site and read the fine print there? I don't know why a bus would be involved unless there is track work along the route but the Trenitalia site will indicate if there is a bus involved.
https://www.trenitalia.com/en.html

The LE and the FL1 are both regional so no need to buy that ticket in advance.

Your post is not real clear but I think you are trying to get to Ferrara? (Not necessarily get to Tiburtina station?)

Perhaps if you tell us the date and time and destination we could help you find the best solution?

I don't use trainline but I see multiple options with just 1 change on April 8 on the Trenitlalia site.

Thank you for your interest, Christine. I arrive Wednesday, April 8 at 6:50 a.m from the U.S. My goal is to get to Ferrara preferably earlier rather than later. Even if everything goes smoothly, I can't see catching the LE or FL1 before 8:00 a.m. Changing trains makes me nervous and I would like to keep changing trains to a minimum. Some of the trainline options include taking a bus from Fiumicino to Termini, or Vaticano, or to Tiburtina. I have traveled in Italy before and find it easier to navigate finding a train over finding a bus. I like the binario system just fine. I have checked the Trenitalia website and the Italo website, but I would have to buy a ticket separately to get to the train stations they leave from (LE or FL1 depending) and figure out how to allow enough transfer time. I can just buy both my tickets at the same time through trainline. I have used trainline before and the app has worked well for me although I have the other apps as well. Depending how long it takes to get to the LE or FL1 train stations (and they look close together on the airport map), I will need to make a selection, perhaps quickly, so I want to know what to expect. I would prefer not to have to change trains in Bologna. I did it once in the past and found it huge and confusing. I was going from a bus to a high speed train. I think I remember descending forever. The more direct, the better from my point of view.

One advantage to Tiburtina is that it is a through station. All the tracks are parallel, and you take an escalator up to the crossover bridge, walk to the escalator marked for your new platform, then take it down to the platform. Termini is a dead head station, so you have to walk to the end of the platform, then to your new platform, then out to your train, so possibly more walking.

FL1 trains go every 15 minutes and take 48 minutes to get to Tiburtina. Leonard Express trains also go every 15 minutes and take 32 minutes to get to Termini. The departures are staggered so they alternate every 7 or 8 minutes.

You are making this much harder than it is ;)

but I would have to buy a ticket separately to get to the train
stations they leave from (LE or FL1 depending) and figure out how to
allow enough transfer time.

No- if you purchase on the Trenitalia app or at a window or kiosk at the FCO station you purchase the whole journey- first leg is LE to Termini then fast train to Ferrara.

Go to the Trenitalia website- put Fiumicino Aeroporto and Ferrara in the departure/destination slots
Start search at 8 am

The options I see are:

8:38, 9:38 and 10:38 LE to Termini then change to a fast train to Ferrara- all with a 25 min change-25 min to change should be plenty of time

Train is direct to Ferrara- stops in Bologna but no change there.
I don't blame you for wanting to avoid changing in Bologna but none of these trains do that

The departures from Termini to Ferrara are at 9:35, 10:35 and 11:35- all direct no changes. Just keep those times in mind so you can adjust as needed when you get to LE station.
If you happen to arrive at the LE station between 8:38 and 9:38 the ticket you are offered there will be for a diff LE- they run every 15 minutes. I would still probably want that 25 min to change at Termini

There is also a 9:42 FL1 to Tiburtina with a 15 min change to fast train to Ferrara but that FL1 makes 9 stops before Tiburtina. LE is direct non stop

I would keep it simple and just plan to ride the LE to Termini- you are at least familiar with that station. Buy your ticket at a kiosk or window or use the Trenitalia app for whichever train is next.

There are NO buses involved in any of these routes

I'm not sure if Trainline is offering you all the journeys that are available

I do tend to make things harder than they are. Thank you for the advice.

You are welcome
Good luck and enjoy your trip!

Christine, thank you again for your advice. It paid off when at the airport. A number of options on Trainline seemed to be sold out and said “tickets not available”. The Trenitalia website had a ticket for the option I wanted. Perhaps since it was two days after Easter, more people than usual were traveling.

I had to change seats (but same car) in Firenze as the same seat was not available all the way to Ferrara.
For other travelers who may be deciding whether to buy a ticket in advance and hope one’s plane isn’t delayed, it took an hour from the time I got off the plane to go through passport control and collect my suitcase until I was walking towards Leonardo Express. Leonardo Express is about a fifteen minute walk from the luggage area, or less. It is very well marked.

Very happy to hear it went well!