Bach's role - organising men not in union? (9)

I believe the answer is:

bachelors

I'm a little stuck... Click here to teach me more about this clue!

'men not in union?' is the definition.
I can't judge whether this definition defines the answer.

'bach's role organising' is the wordplay.
'organising' is an anagram indicator.
'bachs'+'role'='bachsrole'
'bachsrole' anagrammed gives 'BACHELORS'.

Can you help me to learn more?

(Another definition for bachelors that I've seen is " Available men".)

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