Are females authorized to undo their hair bun during range?

Do you mean like your bun gets in the way of your Kevlar so you need to take your bun down? Absolutely not! My unit was 50% female. If we could qualify with our buns so can females these days. If you mean your bun is falling out so you need to take it down to fix it to be in reg, that's another and you don't need a reg to fix your hair. I can't think of any other reason to take your bun out. If you can't handle your hair, cut it.

Hair regs are AR and DA PAM 670-1. However, the undoing of a bun at a range, I think, would fall under the umbrella of the Range OIC/NCOIC, the Safeties, and the NCO/Officer Chain of the Soldier in question.

Honestly, I don't know, but here's a couple excerpts from the Marine Corps uniform order.

"Hair will be styled so as not to interfere with the proper wear of all uniform headgear. All headgear will fit snugly and comfortably around the largest part of the head without
distortion or excessive gaps. When headgear is worn, hair should not protrude at distinct angles from under the edges. Hairstyles, which do not allow the headgear to be worn in this manner, are prohibited."

>Ch 5 4. Physical Training (PT). Medium/short length hair may be worn down for organized PT, except when considered a safety hazard. Long hair must be secured. Pony tails are authorized. When hair-securing devices are worn (i.e. barrettes, small pony tail holders…), they must be consistent with the hair color. Examples of hair accessories not authorized for
securing hair for PT are; scrunchies, bows, ribbons, alligator clips… MARADMIN 504/07

>Ch 5 5. Boots and Utilities (“boots and utes”). When wearing
boots and utes in a PT environment, hair should be secured using the PT
guidelines identified above. When boots and utes are worn in a non-PT
related environment, hair must be secured per the regulations detailed in the
hairstyle regulations provided in paragraph 1004.5.c.1.a-b. MARADMIN 504/07

>Ch 5 6. Hair Accessories. Except in PT situations,
inconspicuous hairpins and bobby pins, if required, are authorized. Hairnets
will not be worn unless authorized for a specific type of duty. Barrettes,
combs, rubber bands, etc. are authorized, if concealed by the hair. MARADMIN
504/07

Maybe this will help when you look in your respective uniform order.