Is it appropriate to wear bangs while hair is back in a bun?

Why not? At the risk of being classified as a sexest old pervert, one of my most enjoyable habits throughout my years has been enjoying people who maintain their appearance to high personal standards. If you feel best wearing bangs, go for it and conformity be damned. The important thing is that you dedicate the time to maintain the style you choose. That's why I chose a "high and tight" for most of my career; run the washcloth through my abbreviated locks and I was ready to attack the world!

I have always maintained that a woman's worst enemy was her hairdresser. "you need to do this or that", "you would really look good if ...". Pick your hairstyle and the way you present yourself in uniform or muftis to satisfy yourself, and if you choose, your loved ones.

Appropriate? Yes, but it's a pain in the kiester to maintain them and to keep them where they're supposed to be (with respect to headgear). Not to mention hot in the summer. If you want to deal with all that, go for it, but I'll pass, thank you.

When I went back into uniform, I purposely grew my hair out so I wouldn't have to mess with all that. An austere-looking bun may not be my best look, but I'm more interested in practicality, especially in a field environment.

You have the answer - Use the regulation. Carry and laminate a copy to keep on your person for the doubters.