A bedrock geology map will not show surficial deposits such as glacial tills, river sediments, and lake deposits. Bedrock maps have to be constructed using exposed bedrock, borehole data, and roadcuts. My guess is that given the areal extent and depth of glacial deposits that much of the bedrock data is gathered during exploratory drilling for groundwater and mineral exploration and compiled by the state bureau of natural resources (as is done in all US states).
Here is a map of the surface geology of Michigan, which, incidentally looks a lot like a topographic map of Michigan, below. This indicates that bedrock is actually hard to find in Michigan.:
As for why the bedrock geology looks like an "onion", it is a basic depositional basin in which the center drops slowly and sediments, over time, accumulate with the oldest materials on the outer edge and the youngest in the center. There's nothing special about the Michigan Basin other than the fact that it coincides neatly within the state's southern outline. Below are the other depositional basins of the US:
The only other state with a basin within its borders is Illinois, whose onion-like bedrock structure looks a lot like Michigan's:
Hope that helps!