Hi Groovecanon,
Welcome to the Apple Community.
Re: I don't want to sign up for premium to listen to it. How do I get a refund for signing up for this?
Seems you would need to cancel the subscription first, to escape further charges
(ie: just deleting the app would not cancel signing up. Free trials would need to be cancelled at least 24 hours before expiry.)
Wondering how you signed up originally. You might need to cancel the same way.
If you signed up online (ie: not with Apple):
You can cancel from this webpage:
https://help.audible.com.au/s/article/how-can-i-cancel-my-membership-online
If it was a membership / subscription billed through Apple:
If you want to cancel a subscription from Apple – Apple Support
If the subscription that you want to cancel is not listed – Apple Support
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Re: How do I get a refund for Audible Plus?
Re: Apple Refunds:
If the money has been deducted (not pending):
How to: Request a refund for apps or content that you bought from Apple – Apple Support
For Apple Pay purchases:
How to: Get a refund for purchases made with credit or debit cards using Apple Pay - Apple Support
For Refunds directly from Audible Plus:
You would need to use their "Contact Us" (orange button) links, and ask at Audible Customer Care.
(Same page as their cancellation info .... link above at the top of this message.)
All the best :-)