Big-headed American coach (3)

I believe the answer is:

bus

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'coach' is the definition.
(synonyms)

'big-headed american' is the wordplay.
'big' becomes 'bu' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'headed' means to remove the first letter (head can mean to remove the top from something).
'american' becomes 'US' (United States).
'us' with its first letter taken off is 's'.
'bu'+'s'='BUS'

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(Other definitions for bus that I've seen before include "People carrier" , "Coach" , "Road vehicle able to carry many passengers" , "Large passenger vehicle - small business!" , "Of projectiles; (go) mad (slang)" .)

I've seen this clue in the Evening Standard.

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