I live in an apartment and my balcony is on the west, and only receives afternoon sun. Is there a way to put a screen or lattice over the plants that are meant for morning sun only so they are shaded and get filtered afternoon sun instead? I'm trying to find a way to get morning sun bonsai to thrive in an afternoon sun area.

An example species is a Satsuki Azalea

What you suggest is reasonable to augment shade. You could use lattice, sheer curtain, shade cloth, whatever would suit your setup. There's no such thing as a morning sun only plant, as it seems you already suspect. It's an easy instruction for plants that can be overwhelmed by too much sun and/or afternoon heat. You may be able to adequately shade, but will the heat radiating around it be too much anyway? Something to consider. In nature, shade is not adjacent to heat baking off of a building.

A bonsai needs specialized regular maintenance for both the foliage and roots to maintain its' shape and ability to stay in a small shallow pot, which could need to be watered twice a day when it's hot, even with some shade. Not that anyone who wants to can't learn, but may not be what you had in mind.

If you just like the look of a little potted tree, it would be a lot cheaper and easier to maintain many other plants that have not been or need to be "bonsai'ed" to live in a (much bigger) pot. That's one of the cool thing about plants, several different ones can look almost the same yet have quite different origins and culture.

Plants also acclimate over time. My advice would be to put out the bonsai as early as you can in spring. As the sun rises higher and higher in the sky, and the rays become more intense, you will give your plant a chance to acclimate to the increasing daylight and strength.