hey hey marothwell
CJean says take the train (trenitalia.com) may take 2-3 hours depending time & stops
flixbus.com or itabus.it or GoOpti a shuttle (goopti.com) are the bus options 2+ hours times and stops your decision.
don't like the idea that cruise companies say venice, and the arrival/departure ports are 2-3+ hours away. it is what it is but i know people get confused with it. look at the day you arrive in trieste and how many other ships will be in port (cruisemapper.com)
click port, type trieste, scroll down to june 2025, see what day you get into port, how many others are there, # of ship passengers
which gives you idea how many others (thousands) planning to do the same thing you are. just things to think about.
stay near the train station (venezia san lucia or piazzale roma), look at booking.com for hotels close by as CJean says. it will be busy and crowded in venice since high season. check-in times 2-4pm and check-out 10-11am. if too early just drop off bags at hotel and roam around, later afternoon many of the day trippers will be leaving.
your flight is later afternoon which is a good thing. usually venice flights leave at 6am morning, that's why it's a pain (we've been there done that). as she mentioned get to airport 2-3 hours before flight, taxi or bus from near train station to airport.
enjoy your cruise and holiday, go with the flow. we've been 4 times and love venice. ask more questions if need be, here to help
aloha