Hello smartin927,
The various places are generally called
Venice Piazzale Roma - the bus and car park adjacent to Venice proper
Venice Mestre - the bus/train station on the main land before the long bridge out to Venice
Venice Aeroporto/Marco Polo - all things airport
It looks like ATVO Line 29 runs from Venice Piazzale Roma to the airport and then onto Cortina for 14-20e (for a random day in June) twice a day
https://www.atvo.it/en-timetable.html
Checking the Cortina Express website they list their departure point as Venezia-Aeroporto Park - Viale Galileo Galilei so you'll need to get from Venice proper to the airport. It looks like it runs once a day for 22e.
https://booking.cortinaexpress.it/from/Venezia/230614/to/Cortina%20d'Ampezzo/?adulti=1
To get to the airport you can water taxi (fast and expensive), the Alilaguna water bus, but most people vaporetto to Venice Piazzale Roma and then take a taxi or a bus to the airport depending on cost, hassle and time considerations.
https://veneziaautentica.com/venice-airport/
Hope that helps,
=Tod