How to simmer bone broth safely with an overnight pause?
You definitely can't just leave it on the stove; that'd mean far longer than 2 hours in the danger zone. (See for example How do I know if food left at room temperature is still safe to eat?)

If cooking until it's done is out of the question, you need to try to chill it. Putting the whole pot in the fridge might not be the best approach, though; it could take quite a while to cool down. Even if that's less than 2 hours, you're going to go through another cycle later, and the time is cumulative.

The best thing you can do is probably to use an ice bath to help chill it faster.