I'm not really the type of person to hold my tongue, but there is a time and a place for everything. For example, do you know the girl well? Like have you had conversations with her or spoken to her in the past? Typically I find that people dress certain ways for certian reasons. Like you said, she doesn't need to wear expensive riding pants, but it may be that she doesn't fully understand riding. Does she take lessons? Does she have a trainer? I asked if you've spoken to her before to know if you know any more about her. It could be that she puts every dime she has into taking care of her horse and can't afford lessons, but would like them. Or it may be that she is really that mean and cruel. You can't know until you try talking to her.
If you see her horse "misbehaving" aka not listening due to improper riding, instead of yelling to her over the arena, wait until she is done riding. Or if you happen to be riding at the same time or in the arena with her, be very kind. This will be easier if you've spoken to her in the past or now. Minor conversations, or even a simple compliment, "oh you horse's halter is really cute!" will make these conversations a littel easier. It is all about approach. Think of her as one of the horses in the pasture that doesn't like to be caught. How would you approach that horse? (I find that comparing people to horses is very helpful for real life situations. xD)
What I would do is then after talking to her once or twice, or just getting on semi-friendly terms with her, ask her very nicely, "May I make a suggestion?" The majority of people (with some exceptions) will either say yes or ask what. You can then VERY politely suggest that "I saw you riding and I noticed your hands were rather high" (start with one thing at a time, don't hound her about everything). See how she takes to just one thing. Explain to her why it makes a difference, and if she is friendly about it, maybe suggest helping her out next time she is riding. Hard headed people may always blame the horse and never consider they are the problem.
Like I said, you don't know her and you don't know her situation. Joesmom said that the rider may not listen, but at least then you know you tried. But I am the opposite of everyone else saying keep out. I can't avert my eyes to something horrible. It is completely about approach, just like it is with a horse you are trying to teach. Some methods work for different horses. Just think of her as a horse. ;)
Side note: I do agree your BM needs to be.....well, things aren't looking good for that barn. I'd do a search around and see if you can find another barn that can offer similar board prices. Or you can try talking to her again. I wish there was some place where you can Report Bad Barn Managers and have them dealt with! Like a court for bad horse people! Haha.
Keep us posted on everything!!!
~He knows when you're happy
~He knows when you're comfortable
~And he always knows when you have carrots.