Origin/reason for the "hit by a bus" phrase
Solution 1:
People will use "heart attack", "plane crash", "fall off a cliff" as ways to describe that death might happen instantly, and the people left behind better be prepared in case that day happens.
This article talks about it: The Explainer Gets Hit by a Bus
Probably in the mid-20th century. The earliest instance the Explainer could find of a bus accident as a generic rather than literal example of misfortune is from Joseph Conrad's 1907 novel, The Secret Agent: "But just try to understand that it was a pure accident; as much an accident as if he had been run over by a 'bus while crossing the street."
Solution 2:
To address "why a bus and not a plane" part of your question: most people have many more opportunities to be hit by a bus than to be in a plane crash, so "hit by a bus" implies a greater chance that this could actually happen (so you should plan for the possibility).
Solution 3:
My colleagues these days prefer to use "hit by a lottery" as it's a more pleasant prospect for the one we might lose. (We still say "high bus factor" though, perhaps because it doesn't name names the way "what if Jeremy gets hit by a bus?" does.)
As for the prevalence of the phrase, a year or so ago a colleague of someone close to me was hit by the proverbial bus, and was killed instantly. There was indeeed a great disruption in her workplace. I think it's still a fairly common thing to happen. I don't know anyone (even indirectly) who was in a plane crash or who fell off a cliff. I know many people who were in car accidents, but most car accidents are not fatal.
The thing about "hit by a bus" is that it's sudden, possibly unpreventable (compared to say, having a heart attack), no warning signs (compared to deciding to work somewhere else) and complete. The employee is utterly lost to you without warning. But if you find it a little creepy, let me recommend "hit by a lottery" - it gets a smile every time.
Solution 4:
The phrase dates from at least 1907 - Joseph Conrad's novel, The Secret Agent: "as much an accident as if he had been run over by a 'bus while crossing the street."
In 1907 you were unlikely to die in a plane crash!