What you are going to have to do is to prove to her that you were on your way out of the marriage anyway, she feels like she is the reason for you leaving and you have to show her that isn't the case. Also you shouldn't delay filing for divorce if you feel the marriage is over, this will show the other woman that you are serious about leaving and that it had nothing to do with her. She may not want to have anything to do with you until you are free so you are going to have to find closure within the marriage so that you can give the other woman your full attention but it's never good to start a relationship with someone else until you get closure and get rid of the old baggage from the old relationship. She may consider giving you a chance if you are divorced and show her that even without meeting her again you were going to leave your wife.
Allow her some time if that is what she needs, she is feeling guilty and doesn't want to hurt anyone because she doesn't want it to come back around to her, explain to her that you don't see her as a mistress or a fling and that you have feelings for her but do not go to her and say that to her until you are divorced from your wife this may be what she meant by not causing your wife any grief. When you can't get over someone you love, your life is in a real state of uncertainty, the worst thing you could do would be to go into another relationship only to find that it too doesn't work because of your problems. So to help you move forward, you need plenty of thinking time to sort out any issues and you need to reach that point where you can accept that the marriage is over and then follow through with divorce proceeding and leaving the other woman alone until that happens. You have to do the honorable thing here because if you do not then the other woman would go into your relationship thinking that the same thing that happened to your wife will happen to her.
You have to make sure that there is no chance whatsoever, that your marriage could be saved. If you didn't have counseling as a couple, you should explore that as an opportunity of repairing your broken relationship or at least leaving on good terms. There have been many examples of couples who have had difficult times, yet have gone on and enjoyed extremely happy lives together simply by enlisting the appropriate help. If there is a glimmer of hope that your Marriage can be saved, you should explore that opportunity but if not then move on the right way and do it the right way. The course of true love never runs smooth, but you deserve the very best that life brings you. If that means having to move on and find someone new, so be it. If it's over, you need to accept it and look for someone else to love. If it means getting back with your ex, well then go for it but not until the marriage is dissolved. There is a true saying and that is - "some things are meant to be." Hopefully, play your cards right and you will never have to worry again that you can't get over someone you love.