The ground may be green or bare. If you have all four wires at the receptacle, you can connect the new 4prong receptacle without having to run new wire.

smh12, the wiring you have is correct, but you will most likely have to change the receptacle itself to one that accepts a 4 prong cord. the wiring instructions with the new receptacle will show you what wires go where.

Is it normal for a home built in 1995 to have a bare copper wire in the back of the box instead of a green wire?

smh, yes it is. the bare copper comes from inside the "romex" wiring of the home. most likely, when the dryer was installed it was a 3 prong, but the builder knew enough to make sure it could be "upgraded" later on ny running the 3 wire + ground setup.

ok, new 4 prong receptacle is installed. Now I guess I need a new box/faceplate in/on the wall...the new 4 prong won't quite fit. Is there any certain kind I need? Is it better to use metal vs plastic? Can you tell I've never done this before...

"ok, new 4 prong receptacle is installed. "
Did you wire the new receptacle without seeing if it will attach to the old box?

Use a square 4 11/16" box, designed specifically for dryer/stove receptacles. We mostly use metal boxes in Canada. Plastic boxes are much more expensive here.
The receptacle is the "faceplate" as you call it.

smh..are you saying the new 4 prong receptacle is installed in the box and the existing faceplate won't fit?

cobraguy- I guess "installed" was the wrong word. The new receptacle is wired and hanging out of the current, too small, box (power off at main). I didn't even think about seeing if I needed a new box...it looked like it would fit the same as the old. I guess I was wrong. I now have a new square metal box to install and still need to get a faceplate for the outside.