Crossword Genius

As a bighead, I had to make an offer (3)

Ross

I believe the answer is:

bid

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'make an offer' is the definition.
(thesaurus)

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for bid that I've seen before include "Invite" , "Try" , "Offer a price" , "Take part in auction" , "Attempt, offer" .)

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