The only time she will be expected to actually use English is with you
You would imagine the OP were proposing to teach his girlfriend Chechen, Finnish, or Lao...or some other language with limited practical application. I suspect, however, that fluency in English would be considered an enhancement to a c.v. in Colombia, just as it would it in practically every other corner of the world.
OP, textbooks are ultimately a poor substitute for conversational practice, and the best way to teach your gf English is simply to speak English with her as much as possible. A textbook should be, at most, a supplement. Since textbook availability is highly localized, it's difficult to make specific recommendations, but I will say look for something published in an English-speaking country by a respected educational publisher: Pearson, Cambridge UP, etc. Locally published textbooks are almost always rubbish. For starters, you might look for Betty Azar's Grammar series (google it: TT isn't letting me embed the link for whatever senseless reason) since that's one that's available in great many countries all over the world.
Edited by: zashibis