Of course, since the AMT kit is remarkably inaccurate (close enough to be "fun" but by no means "right"), you can do pretty much whatever you wish.
The original-series model simply has a frosted glass dome (I always thought it looked like part of a lamp cover, actually). When I built my AMT kit, I just wet-sanded this with fine-grit sandpaper and then coated it with Testors "Dullcote." It was close enough, I think.
Today, I don't think I could be satisfied with anything less than a little bridge miniature inside, though. It doesn't have to be "perfect" and it can be made from just a few bits of plastic.
Say, a tube (probably one of those tubes they put M&Ms in?) with flat panels inside, evenly space (perhaps painted or decorated with decals?) on a laminated sheet-plastic base.
Now for the BIG E coming from "Round2," I'm gonna have a serious bridge interior there... but that bridge is about the size of a silver dollar isn't it? More detail... a captain's chair, a helm console, etc, etc. I hope most of that is provided in-kit, but if not, it shouldn't be too hard to finish it off.
I expect a photoetch set to make it a near-perfect bridge replica, actually. Most of the bridge can be done, pretty easily, with a combination of two molded parts and several photoetch panels... not counting chairs, obviously (which could probably also be photoetch?)