Yep, Amtrak is the only way to do it on a train, but when it's running and on-time it's my favorite way to travel (i'm only 3/5 for on-time in my train trips the last 3 years). The eastbound train leaves St. Paul about 8am and arrives in Winona around 11am, enough time for a nice breakfast and sightseeing.
There are lots of options for the route back, depending on the distance you want to cover and interest in gravel or other distractions. The most direct and road-oriented versions would be to take Wisconsin 35 or on/near Minnesota 62 to Hastings, then something like 55 to 42 to Rich Valley Road and Argenta Trail north and Mendota Heights Road to the river and into town. Here's the map from the 2009 ride - that one had some gravel riding and good hills, especially in the southern section. We missed a turn somewhere and went north short of Whitewater State Park, but were pretty close to the map - 150 miles for the day. We got home at 2am, but with slow riding and lots of stops along the way. With a reasonable pace and meal stops you could easily be home by midnight (though the night riding is lovely).
http://www.gmap-pedometer.com/?r=2974824