If it is, was the bridge as chaotic as it looked in the film? I always found the scene haunting and wondered if this was a real bridge that was constantly being fought over. I know the film was based on the book Heart of Darkness, so I'm pretty sure there was no truth to a mission like that.
The simple answer is no, it was not based on an actual event. Let me preface this by saying that Apocalypse Now is one of my absolute favorite movies, but there is very few things that are depicted accurately in the movie. Without turning completely into /r/TrueFilm, Apocalypse Now is not as much a historical movie about Vietnam War than a depiction of the Vietnam War as a concept, as an idea and how it was perceived by its contemporaries. The Do Lung Bridge scene is meant to symbolize the never-ending circle of the Vietnam War, possibly reflecting on the futility of the sort of warfare carried out in Vietnam as seen through contemporary eyes.
Excellent movie nonetheless.
Previous answers regarding Apocalypse Now from yours truly: