I can offer a number of recommendations on this topic.
First, I use one of these:
It comes with a shroud that prevents light from escaping even when you're using it. You can see light coming out of it if you look directly at it, but it shouldn't bother anyone. I keep one of those light-blocking curtains with me as well and drape that over the whole thing if there's a lot of visual observers around.
As for the screen itself, you can use Windows Night Light to darken your screen and red cast it. BYE/BYN also has a program that can tint your whole screen red, and I'm sure there are other versions out there too.
Check out this thread as well:
This intrepid poster worked out a whole suite of settings for Windows that optimizes the entire system for a dark red screen.
I also use an iPad to control things while I'm at the mount, and there are some really great settings for those. Fair warning, make sure you're in a very dark room before you program these settings:
Settings > General > Accessibility > Display Accommodations
> Reduce White Point > set to 100%
> Color Filters > On > Select [Color Tint] > Set Intensity bar all the way to the right > Set Hue bar all the way to the left.
Now, go back to the Accessibility menu, scroll all the way down, and click on [Accessibility Shortcut]. Check [Color Filters] and [Reduce White Point]. That's it!
Now, triple-click the home button from any screen and a small menu will pop up that allows you to toggle those settings on and off. If you turn these on, and set your phone's brightness setting to the minimum, it becomes difficult to read even at a dark site.
Hope these suggestions help!