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make one's bow,does it mean to begin (like make one's debut) or to quit? or both.
eg,
Our dictionary will make its bow in the spring.
I shall make my bow and go home,I'm very tired.
Thank you very much.
"Bow in" means to make a debut.
"Bow out" (like an actor taking a curtain call) means to quit.
"make a bow" is ambiguous. It could be used for either. "Bow out" is more common though I feel.
make one's bow 
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