I wouldnt write an apology letter....why bring up negatives about yourself from the past, that she can read over and over again, especially on your anniversary? Stick with present talk and let you actions give her glimpses of the future. If you do write something make it encouraging something that causes her to feel love and hope and good about herself.
me: 30 H:30 tgthr:7 m:4 no kids 5 counseling sessions initiated by H as a LR: Oct 2012 long distance marriage b/c of work since Nov 2012 official BD: July 2013 nothing filed 1/1/14 I dropped the rope