With "bio" it is more focus on the concept of a cinema, that they are watching a movie, and whatever place they migh be at is not important. With "bion" the focus moves to them being located at one specific cinema, what they do there being unimportant. So usually the first one is what you want to say.
One often use undetermined form with the preposition "på", which focuses on the action done there more than the location/transport. E.g "gå på restaurang"~"eat at a restaurant" and "gå till restaurangen"~"walk to where the restaurant is".
Will DuoLingo ever accept "movies" or "theater", along with "cinema" and "movie theater"? "Cinema" sounds pretentious and implies "art films" in most areas of the US (yes, there is more to the US west of the Hudson River New Yorkers. :-)) And "movie theater" is redundant. Going to "the theater" often implies a live stage theater rather than a movie theater.