The driving time is about one hour and 15 minutes. We allow 1 1/2 hours from the door of our WDW room to walking into the terminal building**.
Staying at WDW the night before is a family tradition for us. We like to do something onsite (such as go to Downtown Disney/Disney Springs, eat at a resort restaurant, ride the monorail, whatever). It gets us in the Disney mood.
The drive is quiet and really relaxing. Once you get past the airport, in a few miles you find yourself in the countryside on a straight show to the port. You'll see Disney buses returning from the port taking guests back (probably to the airport), and you'll see a lot of people going the same way you are and who are likely on one of the cruises.
We like to pay Disney Cruise trivia on the drive out, and when you go over that last bridge your ship looms on the horizon it's a great feeling.
(**p.s. that total time is for parking at the terminal with the very expensive and very convenient port parking. If you are using one of the other parking areas nearby you of course have to add time for that service)
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