I am not a fan of bands for chinups. I am not familiar with Niki's progression, so there may be overlap between what we suggest. I have gotten a few women doing chins with the following:
Flexed arm hangs
Negatives
Partials
Chins from the top
Dead hang chins
If your trainee cannot do a flexed arm hang supporting her full weight for three or so seconds, then that is where things need to start. A barbell in a rack is ideal for this. Put the barbell at chin height and take as much weight into the hands as possible. If the trainee can support her full weight with her feet off the ground for a few seconds, there is no need to continue with this. If not, working the flexed arm hang off the barbell using the feet for support as needed is a good way to tackle this. Do five second holds for sets of three. Start with one or two sets. Go to three sets. Hopefully using less and less assist from the feet.
Once flexed arm hangs are good, move to negatives. A box needs to be positioned so that the trainee can easily get her chin over the bar without jumping or swinging. Lower down under control. Full ROM. No dropping or relaxing, but it doesn't need to be super slow, either. The first time this happens, do two sets of two or three reps. Eventually move to three sets of four or five reps. Once negatives are good, it is time to move to partials. Start from the top. Chin needs to be comfortably over the bar to start. Go down halfway and come back up. You might combine partials with negatives if the partials fatigue out early. Start with just a few reps here, too. Once halfsies are going well, move to 3/4 ROM chins from the top. A reduction in reps may be required. Once the 3/4 reps are going well, move to a full chin from the top with a stretch reflex at the bottom. Those may be fatiguing to start, so they can be combined with partial reps. Once your trainee can do two with a stretch reflex, she will have a dead hang and may have one before then. Start working singles for a few sets, then scale the stress upward slowly.
No bands. Just bodyweight. The problem with bands is that they give too much help at the bottom. I like the top-down partials method the best. Each component is more or less identical to what you need to do in a chin, but the force requirements start low and go up. Give it a try.