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.
First measure this distance on the light base:
Then check this distance on the existing bracket. (These should be the threaded holes in the bracket).
If those two dimensions match then use the screws B to mount the base to the existing bracket into the threaded holes. You should be able to start the screws into the bracket and then slide the light base over the screw heads in the larger part of the keyhole slots in the base. Then turn the base so the narrow part of the slot goes under the screw heads and tighten the screws till the base is secure against the ceiling.
If the existing bracket does not match then do a sanity check of the new bracket of the measurement between two of its matching pairs of threaded holes as for example:
When you find a pair of threaded holes in the new bracket that match the hole spacing in the light base mark the pair that will be used. Remove the old bracket by removing the two screws as noted here:
Install the new bracket in similar position as the old bracket using the existing screws through the slotted holes of the bracket. Center the new bracket over the box. If it is longer the ends of the new bracket may ride out over the box and rest on the drywall surface. Secure the bracket into place. Then start the screws B into the marked holes. Then, as noted before, slide the light base over the screw heads in the larger part of the keyhole slots in the base. Then turn the base slightly so the narrow part of the slot goes under the screw heads and tighten the screws till the base is secure against the ceiling.
Best Answer
Grab the edges carefully and pull down. Should slide down on metal spring catches on two sides. Once down about an inch, you'll see them. Sqeeze together, like tongs, and pull down and out of the slot in the recessed frame. Some have coil springs but if it's difficult to pull down, it's probably the sqeeze style.