Air carrier Captain reported having a ground conflict with a shuttle bus that drove onto the taxiway. The Captain stopped and the bus drove under the wing.

Narrative

During taxiout we were given a runway change to depart via runway XXL (instead of the expected runway XYR). Ground gave us instructions to taxi via taxiway 1 and taxiway 2. As we were taxiing west on taxiway 1; a shuttle bus that is transporting passengers between terminal XX and terminal XY entered the taxiway by the construction area of terminal XZ. We were moving and had our taxi light on. The shuttle buses did not yield and entered the taxiway driving the opposite direction and drove under our wing. We stopped when we saw the bus entering and not yielding. The bus had zero concern and appeared to be more concerned with getting to its destination than yielding to aircraft. It's a high likelihood one of these shuttles will contact an aircraft with this behavior.