I don't think anyone except BMW knows the true answer.
But, at a guess, I'd say 200 watts. On my bike I use: driving lamps (110W), heated jackets (approx 25W each?), heated grips (10W each?), GPS (5W ?).
I have had to replace the battery, but the problem was that the battery failed to hold the charge, rather than that the alternator wasn't charging it. I can say this as the battery only failed after 18 months, and I've been using these accessories for many months, if the alternator wasn't keeping up the battery would have been flat within a week.