You are slightly lucky then. Substance abuse/detox/mental health companies tend to be nicer on people in recovery than others. I don't know what to tell you on how to sell yourself because it actually often depends on the facility. A local detox/substance abuse clinic actually only hires people in recovery, which is wonderful. As of now, they are only hiring physicians and are at full capacity in the other healthcare fields. So, that's not an option for me or anyone else. Maybe in the future.
My point is, just ask around and ask them how they feel about the monitoring program in your state. Some may say "Yes, please apply." and others maybe be like "No, thanks. Good luck in your recovery though."
I have not been on nursing job interviews yet, but here's what I am planning to mention. I am going to be honest about it. I am going to add what positive things it has to offer. They are as follows:
1) I have genuine empathy and understanding of others with substance abuse issues (and mental health issues, please only mention this if it applies). I don't feel like I am grasping at straws in talking to people going through this--it's natural. I am not saying that I always know what to say, but I do feel as though I do not have to always work at it. There's less belittling the patient/client, therefore, they may be more apt to listen to what instructions you have offer. People who have not gone through this are more likely to say "why did you do this?" or "don't do that", etc. (not all non-recovery nurses are like that, though.)
2) I do get drug screened randomly and averaging 3 times a month (insert your number in that place, it varies by state.) That's actually a great thing for employers as it usually guarantees (unless someone slips, then they are likely to be fired and kicked out of the monitoring program) that the potential employee is clean and sober. You do not know that about other potential candidates. I always looked at it as 'I would rather know what I am dealing with than to deal with an unknown.' Just because someone says "no, I don't have mental illness or I am not on drugs", etc. does not guarantee it. After all, people do sometimes lie. There are some un-accepting people out there and sometimes, people feel as though not disclosing will help them. It's understandable.
3) I am more likely to stay at a job that hires me in the nursing role because I am in a monitoring program. Not too many places will hire nurses in this situation. Be grateful for the job and give them 200%. Someone who does not understand substance abuse, dependency, and addiction is more likely to get frustrated and quit. They have zero obligation to stay and could easily get a job elsewhere. So they might. Please reword this in an interview. I come across as snarky. Again, not all non-recovery nurses will get frustrated, just slightly more likely.
Hope this helps. Good luck in the job hunt!