Recent DUI & job offer

I recently received a job offer as well as a DUI. Perfect timing, right? :/
A week before getting the job offer I was dropping a friend off (who had way too much to drink) after a work event when I was pulled over. I had a few drinks hours before getting pulled over. I was arrested & charged with driving under the influence. I will spare everyone the details of the arrest but I have never hated or felt so disgusted with myself and previous to this I had never driven while even being the slightest bit intoxicated. I've never received a ticket, or even been pulled over by the police for that matter. I have, or should I say, had an outstanding driving record previous to this incident. I take full responsibility for what happened, the law is the law but I do plan on fighting this charge.

My question is, how do I go about telling this employer about this HORRIBLE and disgusting mistake? They have not asked for a background check but they would like to know when I can start & I do believe that one of the qualifications for the position is that the candidate have a valid drivers licence as well as a driving record that complies with their insurance carrier. However, during the interview process and job posting for this position it did not state that it necessarily requires me to drive or operate an employee vehicle. During the second interview with this company they stated that they would like me to run light errands from time to time. The position is Receptionist/Admin Assistant

I have not been convicted & I currently have a temporary drivers permit (which will expire soon) that allows me to drive. I need a world of advice here. A part of me wants to call them and decline the offer but this has been my dream company to work for since I graduated college. I feel like the dumbest person alive. Please any help on what steps I should take would greatly be appreciated.

Please spare me the rude & hate comments. You have no idea how dumb I feel right now.