Of course you're not wasting their time. They are a group that's entire function is to help drinkers to overcome their addiction. They know you don't just go in once and instantly get healed!

Everyone has their own pace of recovery and you will find yours too if you just take it slowly and be firm with yourself - it's not going to be easy, but I'm sure deep down you know that. Also, I know it will be very difficult to not give yourself that "reward" of one drink after a couple of weeks abstinence, but if you know from experience that it will get out of hand, just say no. Try to find another substitute for the drink - try a really hot bath and read a book or something. You could even just drink 1 bottle of 0% alcohol, if they do that where you live.

Anyhow, we all believe in you and care about you! I know it seems dark right now but just imagine how bright the future will be when you're clean!

Very good luck on your journey! Everyone here is supporting you