I've noticed that some of these types of questions have "Have you..." as a possible translation, but this one doesn't. To say "Have you a bit of milk?" is entirely legitimate in English.
you can only start a question with have if it is used as an auxiliary (?) verb, i.e. in the present perfect: "have you seen him?". "Have you a bit of milk?" is not a correct English sentence, since there is no "real" verb. It should be "Do you have a bit of milk?"
You're incorrect. It's not so common nowadays and sounds a bit archaic, but is still fully legitimate and is certainly used in many places, mostly in England. The "real" verb is "have". The more common way to say it, i.e. "Do you have," inserts a second verb "do" and is not necessary. "Have you" as opposed to "You have" is a proper way of distinguishing between question and statement.
Interesting, I don't think I had ever heard this before. Thanks for the information :-)
I did not get this as a question from the intonation...is there another clue. I would have said you have a little bit of milk...as an observation.
Intonation is the only clue, but Duolingo doesn't grade listening exercises on punctuation.