Miami Cruise Port is only 8 miles from MIA at 1015 N. America Way, Miami, Florida 33132. If you take Dolphin Expressway it should take between 15 minutes, although this road can get very busy so could take closer to 30 minutes. The Dolphin Expressway is also a toll road and costs around $2 to cross, you can get to the Cruise Port without incurring the toll but it will take 30-45 minutes traffic permitting.
Many Cruise providers will put on a shuttle from the airport but it can mean waiting for other passengers and while some a free, others are quite pricy per head. A private airport transfer is your safest bet, it ensures that you'll get to your destination on time and services like Blacklane include all tips, tolls, and luggage fees in the final price. No waiting in taxi queues or falling victim to surge pricing!