Air carrier Captain reported having to bring the aircraft to an abrupt stop while taxiing at DTW for a bus failing to give way.

Narrative

Safety incident in DTW with a ground vehicle. Had just recently pushed off XX in DTW. Ramp coordinator instructed us to taxi north via 1 and short of 2. We started taxiing to 2; approaching the service road in the middle of the ramp; a bus was approaching from the terminal to the right of us. The bus was seen speeding significantly through the service road; expecting for him to give way to us; we continued taxiing forward at a slower taxi groundspeed. We quickly realized that the bus driver was not going to give away to us; and the bus decided to drive directly in front of us. I had to make a split decision to bring the airplane to a complete stop; which was a fairly abrupt stop. The bus then also decided to stop after realizing there was an airplane headed towards the bus. After the bus came to a complete stop; I signaled with the aircraft lights for the bus to continue driving since the bus was literally in front of the aircraft and I was not sure if the taxiing the aircraft forward would clear the right wing. After the incident had terminated. We continued taxing to 2. I called Ramp Control stating the flight call sign to which the Ramp Controller responded; I saw that; did you see the bus number" and I responded; "bus XX"Failure of bus drivers speeding through the middle of an alley way during night time conditions is a safety hazard and a threat to flights. These type of incidents needs to be carefully reviewed as it seems bus drivers are not getting the necessary training required and knowledge to know right of way rules of traffic at airports."