I had a very similar light, and the key was this:
Any upward pressure exerted from grabbing the glass created friction that made it not turn.
You want to touch as lightly as you can, near the edges, and try to apply rotational energy only, with no pushing up.
Unfortunately, that is roughly impossible to do if you're reaching so high that you need to press up on the glass to maintain balance. So, you still need to solve the problem of getting higher (and you should NOT climb on anything placed on a bed unless it's highly stable). But if you can get a bit closer, try less pressure, rather than more.
It feels very counter intuitive, but it helped me in a similar circumstance.
One other thing that may help, suggested by none other than @Joel Spolsky, was to try using rubber or latex gloves to allow you to produce more friction without more pressure.
Before you start, make sure the power to the fixture is off (not just at the switch) and, if possible, confirm with a non-contact tester (a few bucks at a hardware store).
D are the screws that need to be put through B, which is the bracket that will be attached to the ceiling box to hold up the fixture.
To see which holes, align the bracket with the holes in the fixture base. Thread screws D through the back of the bracket so the threaded ends stick out front. Which side of the bracket is the back depends on the ceiling box and whether you need the offset on the bracket sticking down or up. (It often doesn't matter.)
C are the screws that hold the bracket B to the ceiling box. Once the bracket is installed, you can connect the wires on the fixture to the wires in the ceiling box (including the ground wire to the green screw on the bracket).
Place the fixture against the ceiling with the threaded ends of D sticking through the holes. Attach with the nuts E.
The threaded tube on A is screwed into the center of the fixture, the nut is then tightened down the tube to the fixture. The remaining parts are removed. After bulbs are installed, the globe is put on, followed by the soft washer, the hard washer and the next nut. Don't overtighten or you can crack the globe. Then the decorative cap is put on and then the ball finial.
Best Answer
Trim rings for can fixtures (which are recessed, but look "flush" from below) are often spring-mounted. The ones I've met either have a pair of "long-legged" springs that go into a slot where they will release if you squeeze the legs together (the trim pulls down from the ceiling several inches and stops on bent-out ends of the springs) or two or three coil springs, where you usually have to unhook one end of the coil spring to release the trim (which is more of a pain.)
Either one can be awkward, so start by being on a secure, comfortable work platform, not precariously balanced on whatever is handy.