The only way he adds no value to the roster is if:
1. The Bears think he won't be healthy at all this season
2. The Bears have a minimum salary RB who can replace his goal line/short yardage production.
Matt Forte is still, IMO, remarkably bad in short yardage situations. I've just come to accept that's his weakness. When he can get into space, he's lethal, but when everything gets compressed, he can't get around people, and he can't get through them. Bush can get through them and get that yard, if he's healthy enough to play.
If the Bears don't have him, they would have to go and spend money + Cap space, or a draft pick, on a short yardage back.