The Wisconsin Badgers are not officially out of the bowl eligible race. Sure, six wins makes them a shoe-in for a bowl but there are plenty of five-win teams that get into bowls with the right circumstances. Wisconsin is actually on a track towards those circumstances but a ton would have to happen for them to be invited.
According to Erik Buchinger, a Forbes.com writer who knows all the ins and outs of how a five-win team can get into a bowl, Wisconsin still has insane odds to get invited. Wisconsin sports writer, Zach Heilprin, inquired of Buchinger and Buchinger responded that the "Badgers need to beat Minnesota and for Mississippi State, Kansas, Buffalo, Temple, North Carolina, Delaware, Army, Temple, Auburn, Kentucky, Florida State, Baylor, Kansas State, UCF, Washington State, Rice, Louisana, and Texas State to combine for a 3-15 record or worse next weekend.