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Is there an entry-level hardtail that comes in red and black? Say, sub £600?
Scott Aspect 750, £550, Red and Black... Job done.
Red Black Silver is my Marin Nail Trail
https://www.highlandbikes.com/34/products/giant-talon-1-mountain-bike-2017-blackred.aspx
I found it using a popular search engine though it's £36 over budget 🙁 
But you only asked so we could say 'why'.
Voodoo Bizango?
Freewheel are selling off a black/red 19" Mantra trail LSL for 1/2 SRP if you're interested.
https://www.freewheel.co.uk/saracen-mantra-trail-lsl-19-inch-ex-brand-sample-bike-rna13819sp001
Banging bike for the cash if the size is right.
£30, bosh 🙂
Well she changed her mind about wanting red and black...
Had a browse through Don Skene in Cardiff at their Specialized Pitch range and tbh I was a bit nonplussed. The assistant reckoned they were more for general riding than actual MTBing and I was inclined to agree, with fairly short general purpose geometry and steep HAs.
After about half an hour of chatting and trying bikes he realised we were going to do actual MTBing so he showed us the "women's" Whyte 604 in some nice but girly colours which was a hit, but a bit big - then we settled on a small 603 in forest green.
She's chuffed to bits with it and so am I, to be honest! Looks like a brilliant bike. Stretched the budget a bit but it's got a decent budget fork (albeit coil but with an appropriate spring), tubeless ready tyres and decent trail geometry. Here's hoping she'll feel more confident on it on the trails with it.