The Bully bonus round rule is one of the many rules that can be applied during the Bonus Round episodes. It generally spawns around floor 4 or 5 for all characters and is pretty common on those floors.
When the rule activates, all enemies with space in their inventory will get a Rock in addition to their usual equipment. This weapon, which the Bully usually has, does damage equal to the dice placed within, once per battle. If the Lady Luck rule is active, the Rock will be upgraded.
These enemies will not have Rocks since their starting loadout uses up 8 equipment slots, meaning that the Rock would not fit on screen:
Even if any of this equipment is removed during battle (for example, Aurora using her once-per-battle weather equipment), Rocks will not appear in their inventory.