It's about 45 min to an hour depending on traffic. We're a family of 6 so I found it cheaper to rent private transportation than go with the cruise shuttle. I used Legacy Limo and was very happy with them. Mears Transportation offers bus service and I have heard others have used Art's Shuttle and were happy with them. I used Mears for transporation to Disney before and they were fine, you just have to wait until the bus fills up.
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arts shuttle is supposed to be an economical way to get there for larger parties. You could also rent a town car or limo. Depends on how many of you there are. Tiffany and FL Tours are a couple, Happy Limo also. You could rent a car/van. Florida has one way drop offs so you are not charged extra. As said above it is about 45 - 60 minutes to get to the port.
No, you should be fine. If you do opt for Disney transportation, you are guaranteed that they wait for you. Personally I prefer a towncar service because they only wait for me which is especially beneficial on debarkation day.