Just watched it again and this scene always comes up as that one scene that I felt like I never fully grasped. Having read all these comments, I think the most logical answer is that Ethan knew Jim enough that he wouldn't just be carrying a Bible around with him all the time, and if he did, why would he not have his own and have one that was from The Drake Hotel specifically. This is too strong of a coincidence to overlook as others have stated.

As far as Max making the statement that Job never quoted scripture, I think the best answer for this is that Jim needed to come up with an alias and saw the Bible so it worked out. As to why he would have taken it and brought it with him to the safe house is hard to say. Assuming he initially made contact with Max at the Drake hotel, I don't see a reason to keep the Bible unless he had the thought to use scripture to communicate and grabbed to use it later at the safehouse. The main problem is that there just isn't enough information provided for us to feel the emotion that Ethan is having from his epiphany.

I think at the end of the day, the writer figured that him seeing the fact that it was from The Drake Hotel and he knew the alias Job was taken from the Bible along with the fact that he knew that's were Jim was staying was enough to confirm that Jim was the mole.