Tough one. Only thing I can recommend is gradual acclimatization.
Random thoughts....
Once you get them to the range a big mistake is to start off with centerfire pistols. Twenty-two rifles are a better start. Some guys think that handing them the biggest loudenboomer is fun. It aint.
See if you can rent a copy of Shane. There's a scene in there where Shane (Alan Ladd) is explaining to the very hoplophobic Marian (Jean Arthur) that a gun is just a tool. Excellent. And I'm always amused by Joey's (Brandon DeWilde) expression when Shane shoots the bottles.
I goofed once by taking a lady friend of mine to an indoor range (LOUD) and I forgot to have her wear earplugs under her earmuffs. Let's not forget that with the hair, and maybe eyeglasses, a lot of sound can get in there and be disturbing. My lady complained about her ears ringing and I smacked my stupid forehead, remembering that I forgot to give her a pair of earplugs, too. Dummy!
Let's remember that ladies sometimes have a lot more sensitivity to noise and whatever (that's why they're ladies) and the noise can be pretty disturbing. You know there are some dogs (even big ones) who are sensitive to loud noises like thunder and will cower and shake under the bed in a storm. I suspect it may be a built-in neurological reaction. I base this on the fact that in a certain breed of rats or mice (forget which), the mere jangling of a set of keys will induce siezures in them.
All turned out OK with my lady friend since she had posted one of her targets in her garage and her Dad noticed it and said, "Good Shooting." About a month later she wanted to go again.
Many firearms instructors have remarked that women seem to be better shots than men. This has been attributed to various things, like better fine motor control and the willingness to take instructions. Probably true.
I close these random (and incomplete) thoughts with this:

There are a couple of anecdotes about that lady carrying a gun around.
Terry, 230RN
PS. That's Eleanor Roosevelt