... If you use the Bidet right there shouldn't be shit left on your ass. And you can do a first wipe with a little TP just to make sure then dry with the rag.

Yeah, if you've got shit on the cloth after bidet use, you've either got something odd going on with your bowels, or you didn't do a good job.

Now, that first one is entirely possible! There's a shit ton of things that can make feces very difficult to clean off with just water. No joke, no snark, it can be a sign of an underlying health issue. Steatorrhea in specific can make a bidet next to useless by itself, and can be caused by something like five or six things other than diet that I can think of off the top of my head.

There's also the possibility that it's a physical thing, like hemorrhoids, or just an unusually crinkly anus.

With that being said, even in those cases, is it better to use a rag you can then wash in hot water and be done with, or have toilet paper that's now wet and easy to tear while you're digging those fingers in and smearing the poo around?

It's just poo. It washes off either way. You still have to wash your hands when you're done. You do wash your hands after, right?

Just to dry