I'm also from CA. When dealing with the BRN it's highly important to respond promptly to all communications, demonstrate remorse and show rehabilitation. Read How to Write a Letter to the BRN
You will soon be asked to provide a plethora of certified documents and detailed explanation. Saying that you do not have a drinking problem may be seen as not taking responsibility. Taking responsibility means saying you made a serious mistake, and you realize that others could have been hurt due to your reckless behavior.
Again, strong evidence of rehabilitation is important, including letters testifying to your character and change in behavior. The point is to show that, due to rehabilitation, you would never again choose to drive while intoxicated.
According to the CA Code of Regulations, professional conduct requires that you report a conviction within 30 days. I would get an attorney, as other posters said, but be sure and find one with experience in nursing licensure. Hope this helps. Best wishes.