The owner is thought to have fled when the bus broke down on the outskirts of the capital after developing mechanical problems near the end of its journey from northeast Thailand, the authorities said.
Police said it was unclear where the arms were destined.
"We are investigating and searching" for the owner, said Police Colonel Kamthorn Ouicharoen.
Thailand has seen a number of grenade attacks in the past linked to political violence and personal disputes, while gun and bomb attacks are common in the kingdom's insurgency-plagued deep south.