Bid at is a common phrase used in auctions and sales. However, there are several other synonyms that you can use to express the same thing. Words like offer, propose, suggest, and present are all viable synonyms for bid at. They all convey the idea of making an offer or proposal. Other options include venture, endeavor, and attempt. All these words signify that you are willing to take a chance or risk in pursuing a certain course of action. Depending on the context, you can pick the synonym that best resonates with your intended meaning. In summary, there are plenty of ways to express the idea of bidding, so choose the word that feels most appropriate.