You may want to consider staying at a hotel near the port that has a shuttle to the port. I've heard other members on this board suggest the same thing, and maybe someone can recommend one near the port. Then maybe you can take a cab or if the same hotel has an airport shuttle, take that from the airport to the hotel.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)