Hi Timothy!
Welcome back to planDisney.
Thank you for sending us this question.
There is always one form of
Disney Transport (or maybe more than one) ready to take us around Walt Disney World Resort. They make it very simple for us! To travel from any of the four theme parks, or water parks, it's usually a bus (with a few exceptions) that will transport us to any Disney Resort hotel, and this will be your easiest way to travel to
Disney's Contemporary Resort from Disney's Animal Kingdom Theme Park. As you have a dinner reservation, allow yourselves plenty of time - at least 60 minutes from start to finish.
If you see a bus heading for Magic Kingdom Park, that is another option. From there you can take a short stroll to Disney's Contemporary Resort, or board the monorail for just one stop.
If time is limited, you could take a rideshare - I have used Lyft many times around the Resort and have found them very efficient, and easy to book - download the Lyft app to your phone, where you'll see all the car options available, with various prices.
If you fancy travelling in style, have you considered a
Disney Minnie Van? You can also book these on the Lyft app. I love seeing the Minnie Vans driving around, with their very distinct red and white livery, and it's so much fun to arrive in one of these.
Please come back and visit us if you have any further questions, and you can
send me a direct question if you wish. We are always happy to help you plan your magical vacation to Walt Disney World Resort!
Sue