Use 'bow out' when someone leaves respectfully, with dignity, especially after failure or defeat. Despite losing, the athlete decided to bow out with his head held high.
Pro Tip 2/3
Voluntary Departure
'Bow out' often suggests a personal choice to leave, not being forced out. She wasn't fired; she chose to bow out from her director position.
Pro Tip 3/3
Final Action
Use 'bow out' to indicate the last move of someone or a formal end to their involvement. After the final episode aired, the actor bowed out from the show.