Most surgeons will use general anesthesia. As you can see from the responses, it's not the only way. I've found that doing the surgery with sedation and local anesthesia leaves you feeling better after surgery with less pain and a faster recovery. Look in to it, but ultimately you need to find a good surgeon! Good luck.
Anesthesia for BA can be done many ways. We use IV sedation and regional anesthesia because it is very safe, effective and less expensive. My anesthetist and I have been working together for 20 years and she is very experienced and good at this technique. General anesthesia is fine but produces more of a "hangover" because more drugs are used and is more expensive. If you have inexperienced anesthesia with IV regional, go with the general for safety reasons. good luck.