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Bidder (noun)
Someone who bids, e.g. at an auction
“The highest bidder shall get the house.”
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Tenderer (noun)
One who tenders (a bid, a contract, etc.).
Wiktionary
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Bidder (noun)
a person or organization making a formal offer for something, especially at an auction
“she was the highest bidder for this rare portrait”
“his government’s preferred bidder for the contract”
Oxford Dictionary