Bashful modesty of company head (7)

I believe the answer is:

coyness

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'bashful modesty' is the definition.
'coyness' can be an answer for 'modesty' (I've seen this before). I'm unsure of the 'bashful' bit.

'company head' is the wordplay.
'company' becomes 'coy' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'head' becomes 'ness' (ness is a headland).
'coy'+'ness'='COYNESS'

'of' is the link.

Can you help me to learn more?

(Other definitions for coyness that I've seen before include "Pretended modesty" , "Affected modesty" , "Shyness" , "evasive quality" , "Arch reticence" .)

I've seen this clue in The Times.

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