I'm with Tazzi on this one...and I would go so far as to say that you do not even need to feel close to this person as I have, over the course of my life, had some fairly intense interactions with mere strangers I just met. ( I know that last part sounds kinda cooky, but sometimes you just 'know' this kind of thing in your spirit - I know the defending statement sounds just as cooky)...ANYWAY, the point being that I would personally take this person aside and would not ask her, but rather, tell her (delicately) that I know what she is doing and that I am concerned about her as a human being. Yes, of course you are concerned about the safety of your unit's patients, but this person will not 'receive' this kind of message...at least not initially. Such a threat of punitive action (because that is how she will perceive it) will only increase her denial and defensiveness. If she has any sense at all, she would already know that you as a nurse would have this concern. This kind of person, involved in addiction and self destruction, needs to feel safe enough to disclose her problem. Even still, you may be met with some resistance/denial or outright disdain for your 'assumption'. If this happens, simply stand firm on what you pretty much know to be true (and back this up with saying that you are not the only one who has noticed this and talk about your history of knowing that smell) and that when she wants to talk about her problems, you will non-judgementally be there for her. Also, remind her that there are other non-punitive resources she can turn to. Having at least broached this topic with her as a co-worker who cares, she now will know that her secret is out - which may serve to begin breaking down the walls of her denial (mind you some addicts, depending on where they are in their addiction, have many walls while others only have one or two).
Of course you will still need to watch her closely while at work and report any errors you see just as you would any other nurse. While that initial approach should be a caring one, she also must understand that you are not going to co-sign her addiction by giving her any breaks you would not give to anyone else.
If you convey this "I'm coming to you as a professional, but a very different kind of professional (not the average nurse who first runs and rats)", I believe you will have done the very best thing SINCE she is not coming to work actively impaired. If she were, then that would be a different story.