My family are foster carers and it sucks but I dislike my foster brothers so...
But yeah, it won't be easy process and you can't just foster one person. Social Services will ask to take on others even if it is just for day care. It's a big responsibility and not only that, it takes a long time too. You have interviews, house checks, police checks, it has to go to panel. And with her parents knowing who you are, they might feel she would still be at risk at your house because she'll still go same school and everything.
The fact that you're her boyfriend may not go in your favour either tbh.