My opinion:
One simple letter, explaining everything ~ what you did and / or didn't do; why people misinterpreted it; why you couldn't respond at the time; why you feel so upset; that you still love her; that you wish she trusted you; that you are upset that she doesn't trust you.
Put everything in, make sure it's clear how you feel, but don't make it any longer than it needs to be.
Do it soon, so that she knows the truth as soon as possible and you can take it from there.
But you must do what you feel is right for you!
Good luck!
