In fact, before Crisis on Infinite Earths (1985), Alfred started working for Bruce as an adult. He first appeared in Batman #16 (1943) as an actor/amateur criminologist whose father had once been the butler for the Waynes, and he became Bruce's butler to fulfill his father's dying wish. With Alfred not around during his childhood, Bruce was instead brought up by his Uncle Philip (a guardian in absentia), Dr. Leslie Thompkins, and the Wayne housekeeper Mrs. Chilton (who was secretly the mother of Joe Chill, the killer of Bruce's parents). All of this information was introduced at different times, but you can find it all in one story in The Untold Legend of Batman (1980).
But then, in 1985, the animated series The Super Powers Team: Galactic Guardians (the last season of Super Friends, renamed to match a line of Kenner action figures at the time) produced an episode called "The Fear", which featured the first ever depiction of Batman's origin outside of comics. In the episode, Scarecrow has attacked Gotham City, and Batman, dosed with fear has, finds himself in Crime Alley and remembers his parents' deaths.
It's here where we learn that not only did Alfred raise Bruce, he also helped train him. (And I think it's worth noting that the shot above looks like it could've come straight out of Batman: The Animated Series. We unfortunately can't say the same of the shots below.)
Frank Miller would use this idea in The Dark Knight Returns (1986), and then like most things he introduced in that book, incorporate them into the DC Universe proper in Batman: Year One (1987).