I was going to say maybe she's embarrassed as well, but seeing as you seem so open with her I can understand that it could just be plain laziness too. Has she told you why she puts them in her drawer? Can't she change her pads/tampons in the toilet to prevent this from happening? Is there a bin in the toilet? I know at the end of the day she does need to be responsible although I don't know what an appropriate punishment would be. I would probably ban her from changing in her room and make it a toilet only thing.

I don't know it's so difficult isn't it? I have "can't be bothered" issues with my 11 yo daughter, she is just plain lazy too and I really need to push her and take away luxuries to get her to respond and even then she has a don't care attitude, it can be frustrating.

Good luck I hope you'll be able to resolve this issue with her.