Fly into Bogota's only international airport. It is very easy to navigate and has one of the best lounges I've ever visited, including a great spa if you need a massage pre-flight!
For those flying from the US, there are direct flights from Dallas (American), Houston (United), Atlanta (Delta), NYC (all airlines), and Miami/Ft Lauderdale (all airlines). Copa and Avianca have flights through San Salvador that are very fast and AeroMexico goes through Mexico City. From Miami, it takes around 3.5 hours in flight. From Texas to Bogota, flight time is around 5 hours.