Yes, there is something you can do to make it right: Forgive yourself. Don’t let that indiscretion, however grave, negatively affect your life going forward. It is in the past and always will be. Focus instead on learning from it and being/becoming a better person because of it. I know the question you’re really asking is, “How can I make my friend forgive me?” The bottom line is, you can’t. The most that you can do is offer an honest, heartfelt apology acknowledging your mistake and how it affected your friend. You can also offer her your friendship going forward, but let her know that you understand that your friendship will be measured with deeds, not words.
That said, it is clear that she is not ready to forgive you. That’s too bad, because the healing power of forgiveness is even more beneficial to the forgiver than to the forgiven. Your former friend may feel she is protecting herself by shutting you out entirely, but chances are each time you cross her mind she feels bitterness, resentment, and anger. Those feelings don’t do anyone any good. To paraphrase actor/writer/Irishman Malachy McCourt (who was no doubt paraphrasing someone else), “ Resentment is like taking poison and waiting for the other person to die.” Even if she has this pain nicely tucked away in some remote cranny of her brain, it’s bound to slip out every now and then. It would surely do her good for that memory to evoke compassion and forgiveness rather than bitterness and resentment, but that paradigm shift is hers alone to make.
It’s also possible that she thinks she’s punishing you by not offering her forgiveness. Despite all the water under the bridge, she might still feel like you haven’t gotten your just desserts. The sad truth is that no amount of punishment will change what happened. The only thing that can change what happened is the way in which she perceives it. You can’t change that. Accept it and move on.