I think you need to talk with her and not email and state, that you are sorry, you simply cannot stop doing what you do when SHE startles you. It is something that you have dealt with for years and you are trying, but your body is not going to change overnight.
However, since SHE knows how you can react to being startled, SHE can stop what she is doing by making some small amount of noise before she approaches you so that you know someone is approaching, as your other co-workers do.
And after actually reading all posts now, you can then also state that you received the suggestion of trying a mirror, which you will do, but that does not mean it will be 100% effective, but maybe with her helping also by making noise and using the mirror, we can work on this situation.