YEP! as Uomo Grasso wrote and linked above, the bus stop is right in front of the airport on the main street outside of the airport and since the airport is quite small, it is a very very short walk, like 3-4 min. As you leave the airport, you want to cross the street, head towards the stoplight and, staying on the left side, follow the curve. Right after the curve (which is where cars turn in into the airport), you'll find the stop for the buses going out of the city.
As for the ticket, you should find a ticket reseller at the airport, get it before you get on the bus. You can't buy tickets on the bus anymore, so either that or download the app ahead of time (called App TABNET) and you can buy tickets for all buses in Tuscany on the app. You buy the ticket, and then have to say you're going to USE it on the app when you get on, because it isn't an automatic thing. It allows you to buy the ticket ahead of time, and only "activate" it once you're ready to get on the bus.
More info on the official site:
https://www.at-bus.it/it/biglietti-e-abbonamenti/come_acquistare.html although the site is only in italian.
