I don't recognise the idea that there might be something wrong with "double prepositions" in English. Obviously it's not true in general, but I can't even guess why anyone would think it true in any context.
For the specific usage OP asks about, it's just a matter of whether we normally speak of things originating somewhere, or originating from somewhere. As this NGram shows, we actually use the first form 2-3 times more often, but there's nothing wrong with the second in originate from outside.
That NGram also shows how rarely we use OP's suggested originate from the outside. What this doesn't tell you is that the outside would be extremely unlikely in OP's exact context, because when we include the article before outside, we're normally referring to the outer surface (of a container, for example).
First off, prepositions are tricky words, and it's hard to talk about all the ways they can be used.
That said...
at
We can use at night to mean during the nighttime:
I was there at night.
(notice how I did not say "at the night," which is what you wrote in your question).
in
We can use in the night to mean during the nighttime or at various times during the night:
Hyenas prowl in the night. (at night would work, too)
into
We use into the night to say that something continues for a long time after sunset:
The partygoers reveled late into the night.
on
You are correct, we don't usually say on night or on the night. However, if we expand the phrase, and stipulate which nights we are talking about, then "on (the) nights when..." is a relatively common construct:
The band liked crashing at our place on nights we played at Live Bay.
I try to go to bed early on Sunday nights.
On the nights when we hear the ice cream truck, we'll go outside and buy ice cream.
Now, let's combine some of these together:
We usually lock the front door at night. However, our roommate Micheal is an actor, and he sometimes works late into the night. On the nights Micheal hasn't come home before midnight, we leave the front door unlocked, in case he has forgotten his key.
Best Answer
Both prepositions are correct but have slightly different meanings here, depending on how the author considers the bus. The interpretation also depends on context1.
"On the bus" considers the bus functionally as a form of transport.
"In the bus" emphasises that the bus is a place.
So if I read that someone "fell asleep in the bus", my first impression is that the bus is not in use (maybe it is abandoned somewhere, or maybe the character in the novel broke into the bus company's parking lot and got on a bus at night).
If I read instead that someone "fell asleep on that bus", I imagine it to be a bus that is in use as transportation, so the character caught the bus and fell asleep while it travelled to its destination.
(so far as I can think, this use of on is limited to forms of transportation. One can be on a bus, on a ship or on a plane, while actually being inside. As others have pointed out, if you said you were "on that house" you would be standing on the roof.