What does the paperwork show for charges on your arrest? Not sure how they can give you a DUI when you weren't operating a vehicle. Sure it wasn't public drunkenness or disturbing the peace? Either way you'll need to disclose it and what you write deserves consideration. Intoxicated on a bicycle might work. Maybe try to avoid "DUI, or ...under the influence," language for automated screening issues...?
Things like this aren't necessarily deal breakers anymore but they are still giant black marks which will be used as starting points looking for trends of associated negative behavior patterns. The regionals are one thing but at the majors the rest of your application must be pretty stellar to have something like this. With a real DUI you probably need to otherwise be picture perfect. And even though things are loosening up now, this industry has a solid history of ups and downs and what is forgiven today will probably be forbidden down the road. I wouldn't lose sleep over it if it's your only blemish.
Best of luck.