This was before the "Alfred raised Bruce" retcon. Alfred just appeared one day because he promised his father that he'd continue the family business. And since Alfred's father was the Waynes' butler...
Not that this explains where either Beagle Pennyworth spent the 2 decades or so between the death of Thomas and Martha and the appearance of Batman. It probably helps that, when he first appeared, Alfred was so stupid you could believe he either forgot his father died or it took him that long to find Gotham City.