Is a letter to get her back a good idea? It might be, but it depends on the circumstances, the people involved, and your letter writing skills.
So she broke up with you, but you weren't ready to be out of the relationship and now you're wondering how to get her back.
Sure, you can try to write her a letter and it might well be successful, but keep these things in mind before you do it.
What were the circumstances of the breakup? Determining whether it will be successful to use a letter to get her back depends on how the breakup went and specifically why it happened.
Was it because you cheated on her? Or maybe she feels that you haven't been treating her well.
Was there something that she just doesn't like about your lifestyle or your personality? If you're going to pen a note to send her you have to take into account the cause of the breakup.
The other important factor is your writing abilities.
Of course you'll be able to put together a better letter if your skills are honed.
  But if you're not a great writer, it doesn't mean that you shouldn't write one.
  It does mean that you need to put a lot of effort into, though.
If you send her something that doesn't even have proper grammar or correct spelling, you're going to show here that you don't actually care.
If you instead make sure that it's as good as possible, and heartfelt besides, you'll maximize the chance of your letter to get her back.