As I've read somewhere, Swahili and English have an interesting parallel kind of difference.
In English, we can say "Go to school/prison/hospital" etc., without an article and this indicates that we are going to the place for the main expected reason, ie. we are going to learn / be incarcerated / be treated there as a student / inmate / patient respectively.
If you work at one of these places or are going there for any other reason, you'd say "I'm going to the school" etc. (or "a"). <
In Swahili, I don't know how widespread the parallel is but I've seen it at least for shule(ni) and hospitali(ni). Of course, it's not an article missing but the choice between the locative variety of the noun and the original form of the noun.
Ninakwenda shule = I am going to school. (I am a student and I will learn there.)
Ninakwenda shuleni = I am going to the school. (No indication of what I will do there, maybe I work there or I am delivering something, visiting etc.)
I don't remember where I read this though, but if I find it again, I'll reference it here.
"rudi" is translated as "return/come back", but can it also be translated as "go back"?
Based on the comment from AGreatUserName above, "Rudi shuleni" would indicate going back to the school building, and "Rudi schule" would indicate going back to further one's education. The missing -ni tells us that it is not returning to a locale, but to an experience.
Either that or Duo messed up again.
That sounds right. In the following example, the speaker is definitely talking about getting to the school building each day, not getting an education in general:
"Huenda shuleni kwa basi, siendi kwa gari."
["I usually go to school by bus, not by car."]
So in the case of "Rudi shule", I guess we can assume the speaker is addressing someone who needs to repeat some classes or start a new course, not get back inside the school building.