Winks at bully before one runs for cocktail (6,4)

'runs for cocktail' is the definition.
I know nothing about this answer so I can't judge whether this works.

'winks at bully before one' is the wordplay.
I cannot really see how this works, but
'bully' could be 'cow' (cow can mean to bully or oppress) and 'cow' is present in the answer.
'before' could be 'e' (I've seen this in other clues) and 'e' is found within the answer.
'one' could be 'o' (I've seen this in other clues) and 'o' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?