A number of years ago, I was involved in hiring a nurse with a drug history -- this woman had not only lost her
license, she had actually been criminally convicted and served serious prison time for dealing! This had been years earlier, in another state, and she had worked v. hard to meet all the requirements necessary to get her license back and resume her career.
When she came in for the interview, she arrived with a large folder of paperwork which she spread out on the table first thing -- documentation of her successful completion of treatment and ongoing aftercare, completion of her prison sentence and parole, references from professionals involved in her treatment and from the nursing jobs she had held since then, documentation from the BON in her original state that she had successfully met every condition and requirement they had set for her to work toward regaining her license, and, I'm sure, paperwork on other things I can't recall anymore.
Her attitude was pleasant and professional; she was realistic and open about her situation/history but didn't get defensive or act embarassed at all -- she treated her drug history the same as if it had been
any kind of health problem that could (potentially) interfere with her ability to practice nursing, not some personal moral failure on her part, and she was (well) prepared to make the case to us about why we needn't be concerned that it would interfere with her ability to do the job we were interviewing her for.
We were v. impressed with her attitude and preparation for the interview process, and ended up hiring her. My advice to anyone else in a similar situation would be to follow her example -- be v. open about sharing documentation of your efforts and progress in recovery, be v. professional and matter-of-fact about your situation, and avoid getting defensive or embarrassed. Other people will take their cues (about how they should react to this information) from you and your own attitude.
Best wishes for your continuing recovery and future employment!