No, after completing an Attack mission (PvP), there is no cooldown period, allowing players to immediately send their Bees on other missions like Harvesting or Hunting. This flexibility allows players to maximize their Bee's activities during a single session.

However, if your Bee dies during a PvP mission where you are the attacker, the Bee will require a recovery period based on its Recovery stat. (the same recovery that is required after a Hunting or Harvesting mission)