Bella's boss' reaction is weird. She sends her off home, just for having a conversation with her husband? That's ridiculous. What's more concerning is that Bella's boss doesn't even acknowledge James' presence in the room - it's like he's not even there, which is an eerie feeling I got during the scene.
They get outside and DPC uses a camera technique called "Deep Focus", where an object in the background also happens to be in sharp focus and be seen clearly. In that scene it's weird - there's that guy with the glasses that's watching them, he's clearly in focus and he's like in the center of the screen. His reactions to Bella and James' conversation are headscratching, because they are concerning and Bella and James' didn't talk anything extraordinary anyway, but his reaction is also an alarming hint.
Which leads us to the theory itself - James' isn't there with Bella in the library, he's a hallucination/projection of her mind and she was talking to herself the entire time. Now what happened to him is up for guess, but the most fitting version is that he's dead and it's something that Bella can't accept - she had a nervous breakdown and has some serious mental issues, so it's easier to explain why she's waiting for him to come back.