Walk away while your pride is still intact. She's with someone new, and no one responds well to ultimatums. People have a tendency to wrongly believe in the permanence of situations. This likely isn't the last chance you'll ever have to be with her. Life is funny that way. And I say this for your own sake, honestly, you seem desperate. No woman has ever found that attractive. Pull yourself together before she sees it too.
After you figure out what you did to make her leave, tell her you still love her, and will be there if she needs a friend, or someone to talk to, then disappear. Not totally, but don't hang around so much that she puts out a restraining order. While all this is happening, move on with your own life, fix what made her leave, so it doesn't happen with the next girl. Maybe you'll get a second chance.