Must I use both cables running to my bathroom fan?
Chances are one cable is the source, and the other is a switch loop. You'd need to safely test to be sure, though. If that's the case, here's what it should look like: 



If you don't have a grounding conductor (bare wire) in your cable, ignore the ground wire in your fan kit. There's not much you can do about it without running new wire. It's probably a low-risk issue anyway.

Sorry your question slipped through the cracks. I hope you got it resolved.