My Cortana does the same thing. Shows nothing and when I try to activate it, it says "Make sure bluetooth is on and that the phone is nearby". I'm using Windows 10 on my phone, I wonder if that has anything to do with it?...
My Cortana won't even work for replying to texts or anything. All of the other Bluetooth features are working, like email and Texts.
Actually, come to think of it, I haven't seen anything come through on the Notification tile, either.
Anyone else with Windows 10 on their phones having Cortana tile problems?
I'm on a Lumia 1520.