Hygiene is taught at home primarily. Mothers, guardians, fathers, etc should strive to get the child into a routine. Routine is what you want to establish. Kids really need for parents to enforce this (like homework). Start with talking to the child about bedtime and morning routines. When she stays with you, have her brush her teeth, comb her hair, etc in front of you. Praise her for taking care of herself. My daughter is ten, and if it makes you feel any better, I have to stay on her about brushing her teeth. We have tried just about everything. Another thing you may want to do is get her some literature on taking care of herself. I posted some links below to help you. The key here is positive reinforcement. Always encourage her and her mother if she will not take offense. Let her know that you care about her too. Good luck! Below are books to her from American Girl

WOW....those EXACT words could have come from my mouth a couple of years ago.  My SD is now 7, but I've been around since age 2.  Her biomom was extremely neglectful as well with the same areas and DH wasnt sure how to deal with it since we had her on weekends only for a long time.  
I was tired of battling it, I firmly told DH to step up to the plate and make sure a few basics got done: Bathing, brusing teeth, brushing hair and basic cleaning.  I explained to him that these things needed to get done everyday, that SD needed to learn how to do these things, that SD needed to understand that it's just something to be done...He agreed, but lets face it...men are men. Cleanliness and girly stuff isnt always second nature to them.    I remember my own dad washing my face with his spit and his handkerchief (gross!)
Anywho, DH would forget, and of course SD would forget as well.  
Instead of constantly freaking out about it, I established a morning rouine: wash face, hands, brush teeth, brush hair, tidy room.
(bathtimes were at night) Your SD's morning routine can be anything that's needed, and can add to it as she gets older-(we added flossing and feeding the fish recently)   And if need be, get a night time routine going to!
Even if these things are on weekends, its showing the child a normal routine behavior.  Teach her to be clean, take care of herself since mom wont do it.
It was simple enough once we got the hang of it- and SD learned that its necessary.  Of course not to say we didnt forget...
So we started a star chart ( I made one up off paper, but I think you can buy them too)
Everyday she'd do her morning routine, she'd get a star...and after like 10 stars, she'd get a prize, or a couple of dollars of her own to spend kind of thing.  It's been priceless b/c SD feels really good when she remembers and it solved a huge problem of needed things not getting done.

As far as the neglect...document everything. The  Take photos as well, document everything you can.   Again, this needs to be your BF that does this, really- ultimately it is his responsibility to care for the child and not pawn off his duties on someone else.  That's not fair either. There needs to be some definite 'step up' from your bf, because ultimately if he were to go into court, there's a very good chance you wouldnt even be called.  I've basically cared for, raised, taught, molded my SD for the last 5 years, when we went to court, I was not even listed on the court docs, except for my salary.You shouldnt have to say a thing to the mom, that's not your battle- let BF do it.  
So make sure he steps up and documents everything, get some routines started-It will make a world of difference!
Good luck!

I just want to add one more thing- You ar by far VERY VERY VALUABLE to this child- the effort you put into her life will be well worth it.  It might always seem like an uphill battle, but you are doing the right thing for the child.  I applaud you wholeheartedly- I SO understand when you feel like you are the only one who really 'gets' what a little girl needs...Teach them both what needs to be learned and you will see a difference.  You are an awesome stepmamma and your SD will grow up loving you for that.  

For some added stepmamma support/advice here's some places I go:

Stepmommag.com ( Step mom magazine)
WorkingMothersMag ( Working Mothers Mag)
My most valuable place is Facebook.com and there are quite a few stepmamma supports on there as well as LOADS of information, chat boards that are all very secure and private.  
These are the places I basically 'learned' how to be a stepmamma...it hasnt been easy, but its worth it in the long run.  

There are also lots of books on the subject as well, check out the library! I'm about to read " Enlightened Stepmother" from the Library.