Replacing shower dome light bulb

Use a flat screw driver and try to detach the glass cover as shown below.

Once done, you should consider replacing the fixture.

You can buy the same from Homedepot.

We have the same fixture. It's just stuck. Pull down while holding the glass firmly and work your fingers around the gasket. It will eventually come loose. We replaced the bulb with a LED so it won't need to be replaced again in my lifetime.

Probably a sticky rubber gasket that has kinda adhered to the cage frame over time. Try spraying a penetrating lubricant (you know, the yellow and blue can with the little tube for the nozzle) into the crack and giving it a few taps. Then try your twist (counterclockwise) method again.