Can you take Amtrak from Bloomington IL to Midway Airport Chicago?

You can, sort of. You can take the Amtrak to Union Station, walk east .3 miles to the Quincy/Wells CTA, take the orange line to Midway (a 30 minute ride, an extra two bucks). All being said, you might be better off taking the shuttle from Bone Student Center (drops you off at the gate, 24 bucks or so, less than 3 hours). Good luck.