Hi Rich - I have had 3 BMBs, with only local anaesthetic each time and No.4 is coming up in a couple of months so I understand the trepidation you feel. I agree they are very painful once the aspirator hits bone. The best experience I had was No.2 biopsy where the doctor cracked jokes the whole way through and distracted me quite a bit (laughter is the best medicine).
I've never been offered general anaesthetic, and I'm not sure what effect that might have on bone marrow function if anything? It would be good to know. I heard recently that research has shown that general anaesthetics can have a permanent effect on memory.
I'm praying that you'll be OK. The best advice that I can give is try to relax.