If you have already had a DUI, it's difficult but not impossible to get hired. A candidate who seldom drinks was stopped after his wedding reception. Even though nothing happened before this incident, over one year later, he is still having problems getting hired. You could try and get the record expunged. You should never bring this situation up in an oral interview unless the panel does.
Many candidates feel they have to do repair work.
It will only bury you. The panel probably won't because this is something that is handled with the background investigator. All the background investigator is looking for is a reasonable explanation of what happened. If not, it can be considered an isolated incident. Pat was in the hiring process recently with LA County.