The easiest way to depart from the airport to your lodging would be the official taxi found right outside the exit at the Taxi stand. These taxis have meters and set rates and will get you to your accommodations quickly and safely.
Uber is the simplest method of travel and works quite well in Bogota! You can also use other rideshare apps like Cabify or InDrive.
For the adventurous traveler, Bogota has an incredible bus system called the TransMilenio.