We know that Alfred calling his employer, surrogate son, and the recipient of his wisdom, "Master Bruce," is incredibly old-fashioned. But what did the term "Master" mean, before it became obsolete?
Master comes from the term maegester, meaning "one having control or authority." So, in the beginning, "master" pretty much meant "boss." Over time, though, "mister" replaced "master," and "master" fell out of favor for most groups of people. There was, however, one group of people who retained the title, "master," from the time of Dickens to the end of the World War I.
There aren't many people today who were ever called "Master" in public. The class system that created it is changing. Robert Graves, the author of the I, Claudius series, was called "Master Robert," when he was young. He considered a normal form of address, until he grew old enough to realize that only the servants used the term. And the servants used the term for a certain type of person - not a member of the nobility, and not a family member of their fellow servants.
However, "Master" is not something you'd call a grown man. By the time they go out in society, adult men should be called "Mister," not "Master." When someone calls a grown man "Master," it's an indication that they see him as a kid - an upper class kid, but still a kid. So the fact that Alfred never stops calling Bruce "Master Bruce," is either insulting, or shows that he feels paternal towards the large man who dresses as a bat and goes around kicking people in the face.