Use your "CC reduction" card + "Resilience" to deny point pressure from "Grumpy Bomb".
BK feels relatively safe you while stunned. "Jumping out" of stun earlier, works like surprise effect & confuses him.
Due to Bomb King's significant lack of ranged attacks and abilities, any sniper or long range champion like Cassie or Lian can counter him quite easily. Just make sure you block all side routes, because Bomb King can very easily sneak in.