Awww bless her! If she's finding it difficult to talk to you about stuff face to face, send her a text or email telling her you can understand that and that she can always contact you through technology, about anything at all. Or you can go all retro and buy a notebook that's just for the 2 of you to use. She can write anything she wants to get off her chest knowing that you'll read it and write back. I know that sounds extreme when you're in the same house but it shows her you're listening while saving her the embarrassment of having to divulge personal things aloud.
Buy her a book, or even a couple of the best rated ones, about puberty.
Always Infinity are the most lightweight and comfortable sanitary towels I've used. You want to get the normal and the nighttime ones. Just because she's young doesn't mean her periods won't be heavy. You can only buy them online but that's easy enough with Amazon. Get her some everyday panty liners too. She's young to use them regularly but I'd get a box of mini tampons too so she can give them a try.
She'll need some dark coloured undies and dark towels for that time of the month (Deep purple or burgundy would be nicer than black maybe?) You can get pants that are kind of absorbent and designed for women on their period. I wouldn't use them without a pad, at least not on the heavier days but they may make her feel more confident at school. Google 'Modi-body'.
Yes to a lidded bathroom bin
If she doesn't already have one get a mattress protector for her bed. She might prefer darker bed sheets too.
Make sure you always have paracetamol and ibuprofen in. She can take them both together. Some people take them alternately 2 hours apart.
Buy her a wheat bag or a hot water bottle
I guess she gets pocket money - is it enough to buy her own sanitary stuff if she feels more comfortable doing that? You can get kids debit cards that you can top up. I'm not sure if they can use them online or not.
Get her a big bar of chocolate, just for her. Hopefully it'll help to break down the wall. Even if she's still fighting you on the outside it's showing her you care.