2 added examples
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In the context of an auction where you are buying something, you place a bid on an item.

Example: "I bid on an eBay auction"

In the context of submitting a proposal to provide goods or services under a contract, you make a bid for the contract.

Example: "The company made a bid for the contract to provide services".

However, when speaking about a proposal to carry out some work and you are referring to the proposed work itself rather than a contract you may gain, you make a bid to do it.

Example: "Walmart have made a bid to build a new supermarket on the outskirts of town".

In the context of an auction where you are buying something, you place a bid on an item.

In the context of submitting a proposal to provide goods or services under a contract, you make a bid for the contract.

In the context of an auction where you are buying something, you place a bid on an item.

Example: "I bid on an eBay auction"

In the context of submitting a proposal to provide goods or services under a contract, you make a bid for the contract.

Example: "The company made a bid for the contract to provide services".

However, when speaking about a proposal to carry out some work and you are referring to the proposed work itself rather than a contract you may gain, you make a bid to do it.

Example: "Walmart have made a bid to build a new supermarket on the outskirts of town".

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In the context of an auction where you are buying something, you place a bid on an item.

In the context of submitting a proposal to provide goods or services under a contract, you make a bid for the contract.