Lighting – Replacing light bulb in an external light

As of 2017, regulatory changes in the United States have obsoleted most of the answers here (and elsewhere on the Internet).

Short answer: Edison screw-type bases aren't going away.

The US Department of Energy no longer considers lamp base when certifying Energy Star luminaires and lamps. Lamp base can even be changed without having to re-certify the product.

The California Energy Commission mostly nullified its prohibition on incandescent lamp usage. Title 24 still requires "high efficacy luminaires" on new construction, but the definition expanded from luminaires that can only use fluorescent/LED lamps to luminaires that could use fluorescent/LED lamps. Notice that most luminaires include a free CFL; this lamp is necessary for the luminaire to meet the definition of high efficacy. The fact that the CFL can be swapped out for an incandescent lamp is now irrelevant.

The slightly smaller dimensions and quicker twist-lock insertion/removal of pin bases isn't enough to overcome the ubiquity of Edison bases. That's why GU24 bases are rarely found outside of specialty lighting stores. It's not uncommon for a luminaire with a GU24 base to be priced $20 more than the E26 variant.

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.