Air carrier flight crew reported a ground conflict with vehicle during taxi at ORD airport.

Narrative

This is being filed for awareness of continued ground safety concerns and hazards at ORD. This past weekend; an employee bus with a company airline logo came extremely close to colliding with an Aircraft X. The Aircraft X; painted with a different company's livery; was taxiing northbound on Alpha (A) taxiway as we were in trail. As the Aircraft X approached near intersection A13; I noticed the aforementioned bus rapidly crossing the intersection so as to avoid having to wait for two aircraft. The bus made its way to either G or H terminal. From our position; the bus came extremely close to colliding with the Aircraft X and our view was rapidly confirmed when the Aircraft X crew immediately reported the incident. Had the bus collided with the aircraft; this would have been a complete catastrophe. To our surprise; Ground Control was going to simply let this go with no further action! If ground vehicles don't have ASDE-X transponders onboard; perhaps it's time to get them retrofitted or come-up with other means of ensuring that this kind of action does not lead to an unnecessary ground collision. Drivers need to be accountable for this type of action; otherwise we will continue to expose passengers and ground personnel to risky driver behavior.