What regulation or policy states that females are allowed to have their bun down in a ponytail while firing at the range?

If FM 3-22.9 stated you could have your hair down in a pony tail when on the range but TC 3-22.9 now supercedes that FM....and the new TC does not clearly state you can have your hair down.....then guess what. No more hair down.

Okay, I think I found the "why" to your question. Here is the excerpt from FM 3-22.9:

"When in the prone position, the IBA's back plate tends to shove the personnel armor system for
ground troops (PASGT) helmet over Soldiers’ eyes. To minimize the PASGT helmet positioning
problem, make sure that the helmet is properly sized and fitted. Female shooters with long hair
will find that wearing their hair in a bun adds material between the IBA and helmet, further
forcing the helmet down over their eyes. Encourage female Soldiers to wear a short (chin length)
haircut or cornrow hairstyle. If the female Soldier chooses not to wear short hair, allow her to
wear her hair down when firing. Tightening the suspension harness and sweat band (raising the
helmet higher on the head) can lessen interference with the IBA, hair, and helmet."

We no longer use the PASGT (haven't since around 2005) and no longer use the IBA (since around 2010). So the equipment limitations that necessitated this are no longer an issue.

It's not mentioned in TC 3-22.9 anywhere and AR 670-1 para 3-2 states that although long hair can be worn in a ponytail for physical training, even if the physical training is in utility uniforms, if the helmet is worn, hair must be secured in a bun. Train as you fight.

None that I am aware of. In Israel the females are allowed to wear thier hair down, but I think it's a mistake. Given everything that is required of a soldier on active duty. They should wear their hair according to the requirements of the regulations. Plus why wear it down if its going to get in the way with what you are doing? It must be neat and feminine in appearance. Be worn above the collar and not interfere with headgear.

I don't ever remember seeing that or even being allowed at the range because all appearance is covered in 670-1.
Faddish and exaggerated styles, to include shaved portions of the scalp other
than the neckline, designs cut in the hair, unsecured ponytails (except during physical training), and unbalanced or lopsided hairstyles are prohibited. 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 bulging or distortion from the intended shape of the headgear and without excessive gaps. When headgear is worn, hair should not protrude at distinct
angles from under the edges. Hairstyles that do not allow the headgear to be worn in this manner are prohibited. Examples of hairstyles considered to be faddish or exaggerated and thus not authorized for wear while in uniform or in civilian
clothes on duty include, but are not limited to hair sculpting (eccentric texture or directional flow of any hairstyle to include spiking); buns with loose hair extending at the end; hair styles with severe angles or designs; and loose unsecured
hair (not to include bangs) when medium and long hair are worn up.