Bush made one start in 13 games during 2012, rushing for 411 yards and five touchdowns on 114 carries. He also hauled in nine passes for 83 yards.
To replace Bush, the Bears re-signed running back Kahlil Bell, who was on the team earlier this season before being released and joining the New York Jets.
New York cut Bell this past week. He has amassed 589 yards rushing on 131 carries over his four-year career.
