3 Bottles seems very low I'm sure they must carry more than that, I fly the LHR - BKK route and I would say I have 4-6 glasses on the way out as its a night flight but on the way back I am awake the whole way and pretty sure I always have in the region of 8-12 glasses easy, had to wait an hour for a bottle to chill once but have never had it run out on me.
Flying again next month so really hoping there is no change to my previous experience onboard with the Champagne