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If you arrive in Bogota at the airport then go to the taxi office and state your destination and they will work out the correct tarriff and you present it to the taxi driver and that ensures you are not overcharged. The cost from the airport to the centre of Bogota is about 18.000COP and a bit extra if it is late at night. This also ensures you are taking a registered taxi and not an unlicensed one which would work out more expensive,uninsured and possibly unsafe.
In Bogota the licenced taxis are metered so there is no problems with cost of journey variances. The transmilenio bus system is superb and a very quick,safe and cheap mode of transport which covers the city. There are colectivo mini buses which are all over the city but where they go to can be difficult to work out. First time travellers should be able to manage it without too much dificulty.