I know part of the reason I didn't want to tell people in the beginning was that I was afraid I might slip or go back to drinking and I didn't want anyone to judge me if I did that.
Maybe I was leaving myself an "out," who knows?
My suggestion is that you not make it a huge formal announcement--just tell her that you miss going out and being with her, but that you have decided you shouldn't drink anymore and you don't feel comfortable right now being around drinking. Tell her you'd love to go out to lunch next week or something.
I'm betting that if she's the good friend you say she is she will be glad you're taking care of yourself and be happy to have lunch with you. And you won't be carrying around all this worry anymore. Really, it will be a big relief. The anticipation is always more intimidating than the reality.