good and solid advice from previous posts. I'd suggest go ahead and starting to draft a statement _now_ about this offence that you could offer the BON. If you do appear they [should] want a statement from you, or for you to have an opportunity to speak your piece. Start this document now; run it by anyone you can think of to get feedback (if you can find people who've been in legal sort of situations or...better...are in defense law, get their opinion ASAP).
I'll tell you some stuff though I learned in school and in orientation for work that is KEY to making this statement poignant:
-Analyze very carefully how you "admit guilt". Obviously there is no question of the conviction, but do not make excuses, but don't throw yourself under the bus...this is a tricky balance to dance with, but the next point can help with that.
-"Remorse" is of utmost importance! Now this doesn't mean grovelling before the BON or anything...in fact that makes (in my opinion) you look less mature in an initial interview. However, demonstrating a sort of regret to the situation is definitely needed. Coupled with the above, this can be a POWERFUL couple/few sentences that play to the humanity of the member(s) reading/listening to your explanation.
-"Aspiration" is also a good inclusion for this type of thing. Why do you want to be a nurse? Why should they license you? Here is an opportunity to sell yourself to them. I would also suggest being humble here. Saying "Epic: Look it up and there is my face, the 2. definition is "epic nurse"" really isn't going to help you win any hearts...but if you can communicate your desire to nurse with an [original/personal] touch, you will have made yourself real...a face to a name.
The key to all of this, in any sincere apology to anyone with the power to "hire/fire" is to Admit, Regret, and Commit in a case like yours.
Draft now, edit often. Here is a simple (non-extensive) example for your situation.
I have come before you to address the issue of my DWI conviction in [year]. I understand that without context, on paper, my misguided assumption that I was sober to drive that night might seem indicative of my judgement as a person, but I assure you this is absolutely not the case. I hope that my lack of criminal record after this mistake can help validate my character. (if you are like a super student include something about how in school you killed it here, "I maintained a 3.5 GPA in school" etc etc). My commitment to this field was not because it is a "guaranteed job" or "secured for life", it is because I believe that my love of the medical field and wanted to be have the most time with my patient's in order to see them through the healthcare experience. I want to be part of that human part aspect of healthcare, close to the patient.
I know this is where I belong, and that the mistakes of my past are indeed past. I assure you I will uphold the standard and trust this board benchmarks and if you allow me to license and practice, my judgement and actions will reflect our commitment to patient care and safety.
highlight points above are key, subtle things referring to my points above that you need to learn. I will not hold your hand as this is not my battle, but I feel like having a degree in english gives me a certain amount of cencerity in what I'm offering. BEST of luck; I'm rooting for you!
(and send me some good energy too hahaha, got a stupid bull-crap DUI that hasn't gone to court yet pending. Haven't heard from the BON and don't think I would/will unless there is a conviction given I didn't blow cause the machines in SC are SUPER