(Edit: thank you, everybody, for the great answers!!!)
(Edit: thank you, everybody, for the great answers!!!)
Librivox has free, public domain audiobooks. The narrators are volunteers, so performance and recording quality varies, but there are some very good ones there.
Some podcasts provide legitimate audiobooks of copyrighted works, generally with similar quality caveats to Librivox. For example, the blog “Readings from Under the Grapevine” has a free, legally licensed recording of the Narnia series (except for The Lion, the Witch and the Wardrobe).
I never buy audiobooks with DRM, even if the DRM is trivial to break. Amazon has made clear their intentions to lock media down ever further. I shouldn’t have to put up with that, so I’m not going to support them financially.
If I can’t find a copyrighted audiobook at one of the DRM‐free shops, I get it from my library, either through Libby or by checking out a physical copy. Not that these would be helpful for someone using Audiobookshelf…
[Not a comment on Audiobookbay specifically, I don't remember having tried that one and it may be great for all I know]
I subscribe to their monthly plan, $14.99/month, which gets me 1 credit per month. If you buy one audiobook a month that's $14.99, using that credit, it pays for itself. I really like using my credits on expensive audiobooks, like $25 or something (I'm basically getting the book at a discount) and then I buy cheaper audiobooks using my credit card.
You can stream your purchased books with their app, but I download the files (everything is DRM-free) and move them into Audiobookshelf. Most of their older books are just ZIP downloads of MP3s, but newer books come in M4B format (one large file with chapter markers). Both work flawlessly with Audiobookshelf.
If you buy an audiobook on Audible (e.g., Andy Weir), you can download the AAX file from Audible and use a converter to convert the file to M4B (this strips the DRM and makes it work with Audiobookshelf). This is in a legal gray-area, depending on your jurisdiction.