The person you have feelings for is telling you that she is committed to her current relationship. That relationship would not work if she is involved with you. As painful as this must feel for you now, it is time to move on. In your letter to her, you expressed your feelings for her. I give you a lot of credit for taking that risk. Often times individuals regret what they failed to do more than what they did.
If she keeps her relationship with you platonic, knowing how you feel about her, will only confuse things. It would not be fair for the person she is involved with to have his significant other involved in this type of relationship. Furthermore, by staying involved with her, even as friends, may prevent you from being fully invested in a relationship of your own. The longer you stay involved with her, the longer you are delaying the grief process. The longer the delay in the addressing feelings about the loss, the more painful it will be in the long run.