We had a 15 hour layover at Bogota from Quito to Houston and almost had to pay $250 for 4 people for the airport exit tax.
We were not aware of this tax but were told that if we stayed less than 24 hours, we would not have to pay the tax of $64/per person for US citizens. The only problem was that the Continental rep wanted to see our ticket stubs for the Quito to Bogota flight on Copa Airlines. We told her we threw it away, as most people do, because we didn't think we needed it but showed her the stamped time of entry by the immigration officer but she rudely refused to accept it. She was the most uncooperative airline personnel I've ever encounter in all my travels. She was rude to all the other Continental passengers and I've already sent my complaint to Continental. Her name is "Lady Mendoza" so you better hope you don't run into her.
Even after going to Copa Airlines to get a copy of our receipt of the previous flight, she would not accept it. it's almost as though she has a financial interest for us to pay the tax. Thankfully, another Continental employee came to our rescue, to the dismay of the other employee and we didn't have to pay $250. But this entire ordeal took an hour to resolve, with my wife going back and forth to Copa, the tax office and Continental, with a screaming 3 year old baby in her arms.
My advice to you is to not go through Bogota because honestly, you're not missing much. If that doesn't work, keep that ticket stub from the first flight and don't have a longer layover than 24 hours. $64/per person exit fee is shameful to any tourist wanting to visit Columbia.