I apologized the one time I was accidentally the "other woman." (Long story, he was a good liar!) It did nothing to keep her from badmouthing me and dragging my name through the mud for YEARS. She simply refused to believe that I did what I did innocently, and part of me can't blame her for acting irrationally in all her hurt. That's to say, don't expect an apology to do anything to heal or control the damage done. That said, if she's open to hearing you, go for it.
As a woman in a relationship now, I can't say I'd want to listen to a woman apologizing to me now. I wouldn't want to give her the satisfaction of closure, bitter as that makes me sound.
In short, try, but not too hard.