Just focus on moving on. Talking to her will only prevent you from doing so.
You two broke up. It's not your business whatever she's upto any more. Why do you do feel that she is going to have to tell you? I know it's not a nice feeling to have to find out that she's moved on so quickly. It's possible that she already moved on a long time ago before the break up or she's enjoying the attention from other guys and healing from the pain in her own way so rebounding. Whatever that is, you don't need to know.
It's too early to think of being a friend with her. You may want to wait till you are completely over her, which means that whatever she's upto shouldn't affect you in any way. That's when you know you've moved on.
Good luck!
“Really, sex and laughter do go very well together, and I wondered - and I still do - which is more important.” - Hermione Gingold-