Bomb King uses Grow after every third attack; however, he does not Self-Destruct as is common for this species. Each stage of growth is accompanied by a change in attack.
At the start of the battle, the Bomb King Bashes one party member for moderate physical damage. After the first growth, he uses Fira; after the second, Firaga; and when he has peaked, he begins to cast Ultima. Counterattacks do not cause Bomb King to grow.
A good strategy is to equip party members with Magic Counter weapons and Fire Eater armor. Once the Bomb King has grown once and begun casting Fira, his attacks will heal party members, but their counterattacks will not cause the King to grow. Using Haste on the Bomb King will speed up the battle using this strategy.