Could you do us all a favour @ForZanyTraybake -
You need to call the council .
You need to explain you will no longer require the second bin. Request that could it be collected from the address, as the person who wanted it is no longer agreeing to pay and you don't want that liability.
Make sure you follow up with them to ensure it has been collected - so that (like you said) there is no danger of blowback to you.
Once that's done, if your neighbour kicks off, then good! You can remind her that this is a paid service. If you don't pay, you don't get it.
I think people are outrageous sometimes in the UK. They get used to something, then expect others to shoulder the costs.
Tell her that if she wants her garden waste collecting, she can make her own arrangement with the council but now will have to pay more money.
Or she can pay you the reduced rate and consider herself VERY lucky as a result.
She cannot however try and sit this out, and hope that somehow the council "won't notice".
If you get billed for this, you'll be fuming - it's all so avoidable.
Just call the council.