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if it's dark red, you'll need to bleach again. but you should wait a month between bleaching

No, purple shampoo will not get her blonde. It won't do anything, it's just for toning out yellow from blonde, it has no lightening properties.

You also don't want to bleach yet.

You need to use colour removers to remove the red dye first. If you're in the uk, colourb4, decolour remover (not stripper) and jo bazz are all good. If you're in the US there's color fix and color oops available, but I'm going to need wicked pixie to come in again and tell me which is the better one as I can never remember!

Once you've done that, up to three times, you can then assess what needs to happen. It really depends what level it gets to and how much red is left. Red often stains though, so it could be very difficult, sometimes even impossible to get a good clean blonde after red.

It is One&Only Colourfix (available at Sallys) that is the better US colour remover.