I think you need to confront her. I could not stay silent about that. Especially if others know I would be furious. Do you not deserve someone that truly loves you and wants you completely. In saying that if you are ok for her to date others then have that discussion too. She may be a polygamist and just loves more than one and can't leave either of you. At least then the secrecy has gone and you can be open about it. It's entirely up to you
If you really loved her that much, you shouldn't have believed what you heard about her so easily and invaded her privacy just like that. Sorry, just my opinion :/ I think you should confront her about this. Obviously she doesn't really love you if she can cheat on you just like that. So why would you want to waste your love and time on a cheating, backstabbing bastard?