Does Bogota Colombia have a postal code?

No we Don't use Postal Codes, neither in Bogota, nor anywhere in Colombia. The reason is pretty simple. All the cities and towns in Colombia are built in a GRID patterns. Our cities are similar to a chess board. the roads that to from north to south are called CARRERAS , and the roads that go from east to west are called "CALLES" . it is similar to the AVENUES and STREETS in Manhattan New York. A typical address in Colombia would be something like.
Calle 26#45-20- Bogota ( the 26th road from east to west, between the 45 and 46 road from north to south, and the 20th house) ( in the city of Bogota)
Carrera 45#67-23 ( the 45th road from north to south, between the 67 and 68 road from east to west, and then look up for the 23 house on that street)