I suggest you hire a car or just get a taxi. I am pretty sure you can get a car service for a reasonable price.
This one: Transportation from Orlando Airport to Port Canaveral : Ace Luxury Transportation
does it for a very reasonable price. But feel free to shop around since this is just an example. The cruise line will also have a transfer option - just remember it is per person and usually ends up being more expensive than a taxi - but check it anyway.
A few weeks ago we took a cruise out of Rhode Island, - just for the heck of it I booked an Amtrak from Boston and then we caught a local bus to the port. Cost: $2.00 (for the bus) per person for a 20 mile ride.
Now - I don't know of a public transportation option from Orlando airport to Port Canaveral - but here is a private shuttle bus company: Port Canaveral Transportation | Orlando to Port Canaveral Shuttles
- cost is $30 per person. But I think a car service would be comparable, just remember your luggage and the tip.