Nobody asks for references outside of minimum wage positions unless they're a small shop.

I've found this to be highly variable over my past few career moves.

My resume indicates that professional references are available upon request.

In my last two job searches, I've had responses ranging from absolutely zero interest in references, to not only requesting the ones I indicated but also asking for even more names and contacts.

Obviously your mind is already made up, but in my experience, it seems the wise move to stay professional in your professional life, even when leaving a bad job.