Uber & Lyft
Both Uber and Lyft are plentiful in Nashville, and they both service the Nashville Airport (BNA).
*At the Airport, follow the signs to "Ride Share" after getting your luggage. You exit the terminal and walk under a covered walkway to the designated pick-up spot for Uber & Lyft.
Map shows it's 6.7 miles the complex (expect property #750 which is about 3.5 miles from the airport.)