Making a bid for something is an attempt to solicit a particular type of behavior from someone else. For example:
"The company bids on the government contract."
Means that the company applies to receive the contract. It does NOT mean the company is bribing a government employee with money!
As an extension of this meaning, a person can "bid" on an item, and offer "consideration" (money) as one part of the bid. However, the bid must typically be "accepted" before it is valid. The point here is that simply offering the highest amount of money is not sufficient to win an activity that involves bidding; it is only one aspect of a subset of completed bids. For example, on auction sites such as eBay, valid bids would also require a user account in good standing and generally a mailing address. In other places, bids may have more substantive requirements.