This thread really helped me when I was asking similar questions, and goes into quite a bit of detail on the math involved.
With respect to the numbers thrown around in in the OP, 20k hands will definitely not necessarily give you a good estimate. 100k probably won't quite end up giving you a +-2ptBB/100 95% confidence interval (depends on your SD, of course), but you'll be getting in the ballpark at the very least.