Why wouldn't he open the bath room door before shooting? He's not blind.
I'm going to preface this by saying I believe he's guilty based on the stories presented so far. That said, why would a person open a door to a windowless room they believe an intruder is. The correct response would obvioudly be to wait until the intruder reveals himself. However, if someone lacked that patience, shooting through the door makes more sense than opening the door.