So how does Amtrak handle this? By running four buses a day, every day, between Madison and Chicago. Yes, the Chicago that's 150 miles away from Madison. Sensible! Moreso than it sounds, actually. For one thing, unless you're coming from Washington, Oregon, Idaho, Montana, North Dakota, Minnesota, or elsewhere in Wisconsin, you're going to have to go through Chicago anyway, and since there's only one route that goes to Columbus, some of those people might end up with long layovers in Chicago waiting for that one train. So you may as well just run the bus from there. The Chicago-to-Madison route also allows them to make other stops along the way: Rockford, Beloit, and Janesville. So it's not as dumb as as it seems at first glance.
What is kind of crazy is that you can't use the Amtrak bus service to get from Madison to Chicago or vice versa unless you're coming from or going to some third destination by train. There is a market for bus service between Madison and Chicago—there are two different companies running that route, one offering service to the airports and another one that goes to the Loop—so why wouldn't Amtrak want a piece of that action? I mean, if they're going to be making the runs anyway, why not try to maximize your ridership?