Yes. The bus from the Tiburtina bus station is the best way to go. Floxbus is only one of the bus companies operating that segment. There is also Infobus, Itabus, Marinobus.
From FCO to Tiburtina station the train is probably the fastest option that is also cheap. Only €8 per person and it takes 48 minutes. Make sure you take the right train and not the Leonardo Express that goes to Termini. A taxi will probably get there in comparable time (depending on traffic) but it’s €50 so I don’t think it’s a great deal unless you have 4 people, in which case it’s not that much more.
You can use the app or also buy the paper ticket. There is no stress in validating the paper ticket before boarding. The validating machines are easy to spot. This is one at the Fiumicino Aeroporto station. Just insert the ticket in the slot and the machine will stamp it with the time and date.
If you purchase on the app do so when you are there, so you are sure you will board the train within the 4 hour window.
The bus station is next to the Tiburtina train station.