I thought more than one of the Amtrak Chicago-Pontiac Michigan Amtrak trains permitted bikes, but sadly it doesn't. (source: https://www.amtrak.com/ccurl/878/628/Michigan-Services-Schedule-103... ) The Blue Water(once in each direction daily) is the only Amtrak Michigan train that allows bikes to be taken onto the train, after you do a bike reservation. Of course I assume by the time the event is done, you'd have to find your own way to spend overnight in New Buffalo and take Amtrak back the next morning at 11:24am, when that westbound Amtrak train arrived.
If you don't mind biking to Dune Park(by Indiana Dunes State Park) from New Buffalo, you also could take the South Shore Line back to Chicago. It's too bad the bike policy doesn't allow people to board/disembark South Shore trains, from low level platform stations. Since it wouldn't be hard to bike from New Buffalo south to either of the 2 Michigan City South Shore stops, and board from there!