All incorrect so far. I'll have to go back and check to see if any meet the requirements but aren't the player though. (the big one i think that'll nullify most of these is the 8th player since 1995 factoid.)
Not Clinton Portis or Troy Hambrick because both had a 100+ yard game prior to 2003.
Not Brock Forsey because there were only 6 100+ yard game rushers for the Bears since 1995 (Brock Forsey, Anthony Thomas, James Allen, Raymont Harris, Robert Green, & Rashaan Salaam).
Not TJ Ducket because there were only 7 100+ yard game rushers since 1995, but a very close and good guess. (TJ Duckett, Warrick Dunn, Michael Vick, Maurice Smith, Jamal Anderson, Byron Hanspard, & Craig Heyward).