The reason I started thinking about "Like Dreamers Do" (and ended up learning the bass part) is that I'd listened to a Roy Orbison album and discovered that the phrase "like dreamers do" is in "In Dreams." This struck me as a unique phrase, so I assumed that "In Dreams" influenced "Like Dreamers Do," but yester-day I did some research and learned that "In Dreams" was released in 1963. Since "Like Dreamers Do" was recorded 1 January 1962, "In Dreams" couldn't have had any bearing on it.
Regardless of that, this bass part has some rhythmic similarity with the bass part in "And I Love Her" (or, to get the chronology right, the bass part in "And I Love Her" has some similarity with this bass part), specifically the two dotted quarter notes followed by a single quarter note.