Bush ran for 139 yards and a touchdown and also reeled in four passes for 34 more as the Lions (3-1) recorded a second straight win.
Matthew Stafford passed for 242 yards, making good on 23-for-35 tosses with one touchdown and an interception. The signal-caller also rushed for a score for Detroit, which improved to 2-0 at home.
The Bears (3-1) saw their three-game winning streak snapped as Jay Cutler hurled three interceptions and lost a fumble.
He finished 27-for-47 through the air for 317 yards and two touchdowns in the loss as Chicago lost for the first time in four meetings with Detroit.