There's no train connection with Bogotá Airport.
Car and bus
Bogotá International Airport is situated 13 kilometers northwest of the city center. The airport is easily accessible by rental car via Calle 26 (also called the Avenida El Dorado) leading directly from the city center to the airport.
Bogotá's express bus service (TransMilenio) is connected with the airport since 2011. These long, modern busses take you in no time to almost any destination of interest to tourists in the Colombian capital.
Car rental Bogotá Airport
You can rent cars in the Arrivals Hall of both terminals. There are three car rental companies present at Bogotá Airport: Budget, Dollar and Flash Rent-a-Car.
There are two ways to rent a taxi at Bogotá Airport. You can just get into a taxi and make sure the meter is running and the driver doesn't make a detour. You can also buy a ticket at the taxi counter in the Arrivals Hall for the destination of your choice. You pay the price stated on the ticket, although each taxi driver will appreciate a tip. Keep an eye on 'helpful' men wanting to place your baggage in the trunk. They often ask exorbitant prices for this simple task.
There are uncovered parking lots outside the terminal building. Shuttle busses connect the long-term parking lots which are further out with the terminal.