On a different thread, you apologised to me on behalf of nurses for the terrible experience I'd had. So now @Cherrypea, I'd like to return the favour and apologise on behalf of the hard-working therapists for this ridiculous 'professional'. An ending session is standard practice, but its purpose is to be used to provide closure to the client when the course of therapy comes to a natural close. I've never heard of a therapist requesting an ending session when a client has decided not to see them anymore, that tells me everything I need to know about this lady, and you've made the right decision seeking out somebody else.
As somebody else said, you've given 24 hours notice of your cancellation, so unless there is a specific clause in your contract stating that a minimum of 48 hours notice must be given, you've done nothing wrong and should politely decline to pay. 24 hours is considered to be "reasonable notice".
Once again, I'm so sorry you've had the misfortune to encounter such an incompetent therapist; in my experience, it's sadly not an uncommon occurrence, but I'm glad you are giving therapy another go with a different practitioner. I shall keep my fingers and toes crossed that this time you are able to receive the support and guidance you deserve from a professional who cares about more than the lack of wall clocks in their practice room.