Ambrose Bierce uses more than one point of view in "An Occurrence at Owl Creek Bridge." What are the two main points of view that he uses?

The only point of view employed by this story is third-person limited omniscient. 

We can tell that Part I uses this kind of narrator because he knows only the thoughts and feelings of Peyton Farquhar.   In the last few paragraphs of the section, readers learn of his thoughts just before he is hanged. "He closed his eyes in order to fix his last thoughts upon his wife and children." He hears the strange, loud ticking of his own watch, and the ticks seems to get further and further apart in his mind, causing him to feel a great deal of "apprehension." We can only know this because the narrator knows his feelings.

In Part II, the narrator knows that "No service was too humble for [Farquhar] to perform in the aid of the South" and that he believes that "all is fair in [...] war." Thus, it is also in third-person limited omniscient.

In Part III, almost the entire section takes place in Farquhar's head, from the time he begins to fall through the bridge until the moment the noose snaps his neck. If the point of view could not provide us with his thoughts, readers would have no access to this section at all.