I have to catch an early-morning bus out of Budapest on a weekday. Can I buy food (a pastry, or even just a candy bar) sometime around 06:00 at Népliget bus station in Budapest? How about coffee?
The BKK has a handy list about points of sale in Hungarian but if you know the word "Közért" means "Grocery store" (roughly) then you can see one open 5am-10pm at the Népliget metró (underground) station. Also, it says the Relay store under ground is open from 4:30am (the one in the bus station above ground opens at 5:30am) and while their primary focus is newspapers, magazines and such they also sell candy bars and similar as you can see on this http://www.lapker.hu/index.php?mid=38 picture on the official Relay store page. I can't remember for sure but they might even have sandwiches.
The Lipóti Pékség (= Lipóti Bakery, VERY YUMMY! not only their pastries but they partner with Cserpes diaries and they have some seriously tasty stuff) http://lipotipekseg.hu/uzletek/ says it's also open from 5am. Similarly, they might have sandwiches but I am not sure either as I haven't been at this location.