I'm assuming the affair is completely over, and you no longer have contact with your affair-partner. (Your wife shouldn't be forced to communicate with the affair-partner if she doesn't want to....not sure if I understood all of the information you gave) Why not let her scream and yell at you? Listen to her and let her pain really sink in. Experience this moment fully so that you will understand her better and you will always remember what it feels like to see her hurt this badly. Try to grow from this. Hopefully it will be incentive to never repeat your actions.
You could try writing a letter if talking hasn't worked. I would be prepared to tell her what you're willing to do to stay married to her. But right now, she might need time away from you so she can vent and gather her thoughts. Maybe she would like for you to live somewhere else for a while or sleep in the basement. She has been disrespected. Important promises have been broken and she may not be able to trust anything you say right now. She might even have horrible mental pictures running through her mind. Your wife thought she was in a monogamous relationship, but now she has to consider what she could have unwillingly been exposed to, in terms of sexual health. Did you acknowledge to her that she is well within her rights to be irate? I would assume that you've volunteered to go to therapy as soon as she's ready and for as long as it takes. If your wife chooses to stay with you, both she and the therapist will now expect you to make large efforts to instill trust and accountability. There are several behavioral changes you'll need to make to prove yourself, and you need to expect this to take a long time. You won't be in a position to complain about having to answer to her for quite a while. Does she know that you realize these things?
If she decides she cannot see a future with you anymore, you need to make sure she knows that you will do right by her. Bottom line is, she is experiencing shock, betrayal and anger right now. You need to let her feel those emotions. If you want to win her back, you need to be able to apologize over and over and do whatever it takes to help her trust you again someday. You'll need guidance from a therapist and you'll need to understand why you behaved the way you did. I'm sure you know that marital problems are never an excuse for cheating, but therapy will be a way to identify any unhealthy patterns that could have existed pre-affair.