We have tried twisting both ways, pulling etc. No screws visiable. Sorry for awful photo, it's pitch black in the bathroom now!
I see what appears to be threads at the top of the cover/diffuser. A counter-clockwise turn should remove it. I also see paint and drywall mud that MAY be preventing you from turning the diffuser.
The glass part should screw off from the metal part.
If it's stuck, try tapping the glass sharply (as hard as you dare!) with the handle of a large screwdriver, or something similar, while you try to twist it.
It might help to wrap something like a leather belt tightly round the glass, to get a grip on it all the way round.
Be careful if it seems like you are unscrewing the metal part from the ceiling. If that starts to happen, there is a chance you will short circuit the wiring inside and trip the breaker on your house lights when you try to switch this one on.
Try turning it counter-clockwise instead of clockwise like someone suggested before. Also, try to get the glass of first, and then the rest. It seems like you're just having issues with the ceiling :( If it's stuck, maybe try to push it out with something flat and sharp. Maybe a knife would get it moving?