I think you should pretend to approve of her new friends - or at least not to actively disapprove IYSWIM.
Also pretend that you generally trust her and let her know that you're glad she has lots of friends and has fun. IYSWIM. That way she's less likely to do stuff for the sake of rebelling against you or because she's in a hurry to seem grown up and more likely to do things just because she enjoys them.
Make sure she knows you love her and approve of her just for being her (even though your nerves are in tatters) and compliment her briefly for anything you can think of. In other words, try to boost her self-esteem as low self-esteem is at the root of many harmful behaviours.
Also tell her that your only concern for her is that she is safe and happy in herself and that you will rescue her with no questions asked if she's ever in a situation she wants out of quickly. Agree a codeword she could use to save face if need be.
Apologies if you do all this already. It's always my advice as I think there are probably lots of teens who feel their parents disapprove of them or are only interested in them if they're 'behaving the way their parents want them to' - teenage brain etc
In this particular situation could you pre-empt her with some cunning of your own by pretending that you've been in contact with the approved friend's mum, who happened to mention that she's going out on Saturday but she'd love to have your DD/you round another day soon?
And take up the other posters suggestions of providing a tempting - or compulsory alternative?
Encourage the new friends round too so your home is a welcoming place for your dd and her friends.