How to coach half the family? (6)

I believe the answer is:

busily

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'how' is the definition.
Both the definition and answer are adverbs. Maybe you can see an association between them that I can't see?

'coach half the family?' is the wordplay.
'coach' becomes 'bus' ('bus' can be a synonym of 'coach').
'half' means to take half the letters.
'family' cut in half is 'ily'.
'bus'+'ily'='BUSILY'

'to' is the link.

Can you help me to learn more?

I've seen this clue in the Evening Standard.

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