If your flight departs at 06:00 I doubt it is an international flight, but instead a flight to another European airport, where you'll connect to the "long" flight home (don't know where that is for you, assuming US.) Also, don't know location of where you're staying, or how much baggage you have, which will affect the answer to your question.
However, generally speaking, the first bus from Piazzale Roma to the airport leaves at 04:20, and gets you to the airport just as it's opening. You can either walk to Piazzale Roma (if close enough and not too much luggage) or take the "N" vaporetto, which runs throughout the wee hours of the morning. If your lodging is close to an Alilaguna stop (different from vaporetto), you could do that, but I believe the earliest one gets to the airport a bit after 05:00, and you still have a bit of distance (maybe an additional 5-10 minutes, again depending on how much baggage) to get from the Alilaguna dock to the airport entrance (the bus drops you off right in front of the airport terminal.)