Bergamo train to Marco Polo

The train stations named for Venice are either Mestre station, in a nondescript town on the mainland, or Venezia S. Lucia station, which is actually in Venice. Just to get to the airport without seeing Venice, go to Mestre and then take the airport bus from that train station.

If you have time to see something in Venice, you might stay near to S. Lucia station or to Piazzale Roma from where airport buses depart, each just across a bridge from the other. Buses take 20-30 minutes and start about 5:00 a.m. See schedules from two competing services at www.actv.it and www.atvo.it.

I've never been to the Venice airport myself.

Rome2Rio.com is suggesting a train to the Mestre station (Venezia Mestre), then a bus from there to the airport.

You can check the rail schedules on the Deutsche Bahn website. It looks as if your fastest options involve a change in Brescia, rather than in Milan. Travel time to Mestre will be from about 2 hr. 50 min. to 3 hr. 20 min. You'll need additional time for the bus to the airport, or you might consider staying near the Mestre train station if you don't have an extremely early flight. I haven't checked, but a hotel near the Mestre station might be quite a bit cheaper than one out near the airport.

Mestre's not a particularly interesting place to stay. If you have a late departure from Venice, it might be worth spending your last night in the city itself, in which case you'd want to take the train all the way to Venezia Santa Lucia.

ACTV bus schedule, Line 15 from Mestre RR Station to Marco Polo Airport ("Festivi" are Sundays and holidays)

ATVO bus schedule from Mestre RR Station to Marco Polo Airport ("f" is weekdays; "F" is Sundays/holidays)

We've taken two options to the Venice airport:

1st time - stayed at a hotel near the airport. There wasn't a restaurant close to our hotel. Luckily, we had a few snacks left in our suitcase to eat that night. We arrived early to the airport the next morning - hardly anyone at the airport.

2nd time - stayed near San Marco and took the Alilaguna water bus to the airport. This was a MUCH nicer option! If you don't want to haul your luggage over bridges in Venice, the Hotel Ala is located near a boat stop - no bridges between the hotel and the boat stop.

1st option was the Mestre Train Station
2nd option was the Santa Lucia Venezia Train Station & then the vaporetto to Hotel Ala.

I will be on a tour that ends in Venice. My extra few days afterwards will be in Bergamo with a day trip to Brescia. Since my plane leaves Marco Polo at 12:45, I prefer to stay some place closer to the airport with easy travel to get there.

Take a train from Bergamo to Venezia Mestre station (Mestre is a district part of the city Venice, but in the the mainland).
Staying in Mestre, the mainland, is a better choice since you will have seen Venice already and from the mainland it's quicker to the airport.
You will actually need two trains because you need to change trains at Brescia.
For timetable use:
www.trenitalia.com
For station names use the Italian names (from Bergamo to Venezia Mestre).

Once at Venezia Mestre, you should go to a hotel either next to the station itself (where you'd walk) or to a hotel close to the airport itself (by taxi from the station). That choice is up to you.
If you intend to have another glimpse at Venice on your last day/evening, maybe you should stay near the Venezia Mestre station. From there you can take a 10 min train ride to Venice itself. If that is your choice I recommend one of these two hotels, both across the street from the Venezia Mestre station:
http://www.hoteltritonevenice.com
http://www.hotelbologna.com
From either hotel to the airport it's a very short taxi ride (20 min).

If you don't care to see Venice again, and you'd rather stay nearer to the airport, then when you arrive at the station (Venezia Mestre), take a taxi directly to the airport hotel of your choice. I recommend the Courtyard by Marriott (see website below):
http://www.marriott.com/hotels/travel/vcecy-courtyard-venice-airport/

The courtyard by Marriott offers a shuttle service to the airport for only 2.50 euro per person.

There is a modern Crowne Plaza near the airport in Quarto d'Altino. The train stops right outside (no, really, right outside) so arrival should be easy. I've stayed there - free parking - and it is reasonably convenient to Venice. I understand that they run a shuttle to the airport but I know nothing about it, or I am sure you could take a quick taxi.

The breakfast is fairly generic Italian Holiday Inn plus, including of course the breakfast cake.

The rooms are very soundproof. Overlooking the tracks we only knew the trains were there when we opened the window and looked out.

I suggest that one because of arrival ease and personal experience. I don't know that it is any better or worse than the Courtyard.

I've just remembered, when we were there several years ago the wifi in the lobby was much better than the wifi in the rooms. Several years on that may have changed.

Thank you all for your help and suggestions!