How fast can we spin a large-diameter ring levitated by a well-designed and uniform magnetic field before running up against the laws of physics?

I don't understand what you mean by "bandwidth". You might be using that term in a way that makes sense, and I just don't see it, so I'm not qualified to answer your question. I will assume you mean physical thickness, a ring that is 1 meter across its insides, but hundreds to thousands of km across the whole thing.

If you're talking insurmountable engineering challenge with today's technology, it looks hard.

Build a circular railroad track, elevating it wherever necessary. Possibly you could do it across the north american Great Plains, or maybe a great big plains somewhere else.

Put a bunch of light-weight railroad cars with sufficient engines on the track, enough to mostly cover it. Put your giant ring on them. You can spin it at the rate you can drive the engines. This can be done with 19th century technology, if you can handle the expense. The ring itself can be made of cast iron and tin in thin shells, preferably with some rubber spacers or springs to handle nonuniform motion by the locomotives. You can spin it as fast as you can run your engines.

Once you have your circular railroad tracks you can put up your magnetic bearings and maybe spin it faster. I'm not sure how fast it could go. Problems would get inherently too big at some point. If the ring depends on tensile strength of the metal, at some point your ring breaks. How strong can you make it? An engineering question. Maybe you'd run into giant problems before that.