I'm not sure how old you are, but I'm going to assume you're quite young. Not important. Just trying to get a grasp on what stage in life you're experiencing.
You need to understand that someone committing suicide, especially over a two day "relationship" is in no way your fault. She obviously had mental problems before this situation. It sounds like she was on the edge and this was just what sent her over.
Sure, you provided the information that her boyfriend was seeing another girl. But I feel doing something like that, especially for a friend, will always be the right course of action. No matter if your intentions were less than friendly. I think shes fortunate to have someone honest enough to tell her. The truth hurts more times than most. But for me, finding out people who claim to care about me were hiding shit from me hurts even worse. I'd sooner kill myself over secrets than I would the truth about something.
It almost sounds like theres some sort of jealousy/competition between you two when it comes to boys. I could be wrong (it happens) but the fact that you assume she wanted you two separated because he would "like you more" makes me think that. As well as you needing to tell her the guy was betraying her. I kind of imagined you menacingly rubbing your hands together and possibly laughing maniacally (bwahaha) when you told her. But thats not to say you wanted her to commit suicide. Just maybe cry into her pillow a little as she rethought her priorities and young life so far.
At the end of the day, you're not responsible for her attempted suicide. Other forces (parents, genetics, her life experiences so far) hold much more blame than a little fight over some guy. But how good a friend you are to her now could mean the difference between her seeking death again or finding reasons to live life and learn to love it again.
You have a choice. Be a friend and help her back to her feet every time she falls, or cut your losses so you won't have to live with guilt every time she has a mental breakdown.