Check the schedule for the Metra Union Pacific north line running from the Ogilvie Transportation Center, (OTC) 500 W Washington. It is the commuter line with lots of trains from Chicago to Waukegan; fewer from Chicago to Kenosha. Metra has special bike cars, but bikes may be restricted at certain times:
https://metrarail.com/riding-metra/bikes-trains
The schedule, map, and fares are at:
https://metrarail.com/maps-schedules/train-lines/UP-N
My wife and I used it on a bike-train-boat multimodal. trip including the ferry from Muskegon, Mi to Milwaukee, WI