bus to and from FCO - Termini?

Why not take the train?
Leonardo Express
Very simple runs every 15 min
14 euros
No need to purchase in advance

https://www.rome-airport.info/leonardo-express.html

There are a lot of YouTube videos showing exactly how to take the Leonardo Express
Here is one:
https://m.youtube.com/watch?v=L8TE7R2AEUk

The bus appears to be 5 euros

Also does anyone know if the 72 hour public transit pass includes the train from FCO to Termini? There appears to be a 72 hour pass which excludes the "non stop" train from the FCO airport to Termini but is there another train that has stops that would be covered by this?

Pretty sure there is no pass that covers the train

Here is bus info
https://www.rome-airport.info/bus.html

There is another airport train, the FL1 that costs 8 € per person. It doesn't stop at Termini but at Roma Trastevere, Roma Tiburtina and other secondary stations around Rome and the districts surrounding the city center. It's not covered by any pass.

On top of trains there is a metro line connecting Roma Tiburtina and Roma Termini, it would be covered by the ATAC passes and tickets.

Buses are buses, check which one is departing to Rome first, buy a ticket and get on.

We have used one of the coach shuttles from Fiumicino to Termini in the past. It was fine; we just bought the tickets at a kiosk outside baggage claim when we arrived but I see that virtually al of them allow purchase onboard the bus.

https://www.adr.it/web/aeroporti-di-roma-en/pax-fco-bus

I don't think it matter which one you choose if you're going to Termini,.
Editing to add: I would probably pre-book your bus seats back to Fiumicino to catch your flight home. I say that due to some recent taxi strikes probably putting some stress on other transport options. Don't know when/if the next one will be but good to be prepared, maybe.

We took a bus from FCO to Termini last trip there in 2019.
We bought the tickets from a kiosk outside the airport, along the area where all the big buses and taxis were.
We initially got in line for the wrong bus, so you just have to watch where your bus leaves from.
It was easy: just as easy as the Leonardo Express train, and much cheaper.

None of the Metro passes cover the Leonardo Express.

The trainline.com seems to be offering much lower price tickets on the train from FCO - Termini.

Has anyone ever booked this?

Trainline is a third party reseller
Hard to believe they would be less expensive for the Leonardo Express

It could be the regional that goes to Tiburtina NOT Termini ( see Dario’s post above)

Best to book on Trenitalia
Best to wait til you get to FCO
It’s a pretty simple thing that you are making more complicated just to save few euros

Lotus, if you really want to save a few euros, just use one of the coach buses I linked in a previous post. It is not difficult. And no, I would not use Trainline for booking tickets on the Leonardo Express.

I didn't do a deep dive but those $8.60 fares you're likely looking at on Trainline are not for the Express. They are trains which either involve a change at Trastevere before Termini or they go to Tiburtina and not Termini. The $15.05 fares listed are likely for the Leonardo Express.

yeah we took the bus it was fine.

maybe it takes 15-20 minutes longer each way (compared to train)