I'm a BS, so I hope you don't mind me replying....
Please respect your wife's needs right now, she's hurting beyond what words can ever explain. If you really do love her, give her the space she has asked for. She needs to process what has happened; at the moment, you're a reminder (we call it a trigger) of what has shaken her world to it's core. She probably feels the need to run away from that right now.
Give her the time she needs, and use it well; work on you. Work on understanding what has led you to this point, work on setting new boundaries for yourself, and changing the behaviours that led you to an affair.
If you have started to do the work, and she decides she wants to talk, be open and honest, and tell her what steps you have taken to make you a safer partner.
My friend, it will take time, and lots of it, to get to a better place. I can't guarantee that your wife will want to reconcile, that's completely her call. However, doing the work is not only for her and your marriage, its for YOU.
Good luck, the posters here are awesome, they know what's what.