The Millenium will probably dock in the commercial dock area of Venice. This actually part of the island(s) that make up Venice and it is accessible for land vehicles to take you across the bridge and causeway to the Marco Polo airport which is on the mainland.
Check out this web site which has lots of information and links about Venice.
http://www.europeforvisitors.com/venice/
We ended a Med cruise in 2003 in Venice and stayed over for 4 extra days and still didn't feel like we saw everything we wanted to.
Here is the link for the Venice Marco Polo airport.
http://www.veniceairport.com/?lan=en
I would be surprised if you can get a taxi to take you to the airport for less than Celebrity can take you there on a bus but you can sure try.
I found the following information on a web site on transportation from Venice to Marco Polo airport,
Taxi rank is outside the main entrance or Tel. Radio taxi: 41 93 62 22
approx. 20 mins
approx. 70 EUR
As far as I can tell Radio taxi does not have a web site that is easily accessible.
Have a great next cruise.