I like general anesthesia -- you go in, one moment you're lying on the gurney and the next moment you are talking to the nurse and realize you're all done. In other words, there is no sensation of time passing. It goes in such an eyeblink that more than once I've come out and asked "have they done the operation already?" The only thing I would request is that they put something into your IV for nausea. It's pretty common to get queasy if they don't. Good luck!
Don't worry about the general... You will be just fine. It is pretty normal to have a biopsy done (I had one last year in May) and I ended up having a Leep done to remove the cancerous cells from my cervix. I think that if you have any concerns about the general that you should consult your doctor about it. They can help put your mind at ease.