It fits better if you can take off your front wheel. I also advise putting it above the seats where you will sit, if possible. Enough of the bike hangs over that others sitting underneath will feel a little nervous. If that's not possible, you don't have to worry about it falling, but the folks sitting there will still look at you with a little bit of "Really?"
Ed Barsotti, ED of League of Illinois Bicyclists, and I use this service frequently for downstate meetings, particularly the Lincoln service. Amtrak+bike saves us a lot of money over driving. Ed's 6' or so, rides maybe a 58cm Trek 700c bike, I'm a head shorter. Neither of us have had any problems and enjoy being able to do this.
Sometimes, a conductor will allow you to put your bike in the handicap accessible space, but that's the exception.
The Lincoln service hits 110mph now in a couple of sections. Makes you want to throw your hands up and say "Wheeeeee!" Enjoy riding in Chicago!
Steve Buchtel, Executive Director
Trails for Illinois