Some types of compact fluorescent (PLL, PLT) have a push-in fitting. Try pulling straight out.
Photo by ikiwaner, Creative Commons Attribution-Share Alike 3.0 Unported
I'd try undoing a similar bulb in a similar nearby fitting to verify that the fitting is a normal Edison screw (unless you are in the UK, where you might have a bayonet fitting that needs to be pushed in 2 mm then turned ~20° widdershins).
P.S. While you are working on that, you really ought to fix that loose earth/ground connection with a bolt, nut, washer and maybe a crimp-on ring-connector. Or something similar. —
P.P.S. broken compact fluorescents may need special cleanup