Aside from the very first novel I didn't find any mentioning of the broom riding classes. In the first book Malfoy taunts Harry in this class to get into the air with him, which after a series of events results in Harry ending up in the Quidditch team. However this class will never be mentioned again as far as I'm concerned throughout the books nor the movies.
Was it just a 1-2 hours long introduction? Is there no PE class at the school?