You can withdraw your bid without losing the bid bond if you can prove the mistake was a clear clerical or mathematical error, not a judgment error, and the county has not yet awarded the contract.
For federal bids, FAR 14.407-3 covers mistakes in bids after opening. The county will have its own procurement code or regulations that outline the process for handling bid mistakes. You need to provide clear, convincing evidence that the error was a factual mistake, like a miscalculation or a transcription error, and not an error in judgment about the cost of materials or labor. This evidence usually involves your original work papers, spreadsheets, and any other documentation that shows how the incorrect unit price was derived and how it differs from your intended price. The county needs to see that the mistake is obvious and that enforcing the bid as submitted would be unconscionable. If the county agrees to the withdrawal, your surety company is off the hook. If they don't, and you refuse to perform, the surety company would then be obligated to pay the difference between your bid and the next low responsive bid, up to the penal sum of the bid bond.