You are bound

Your action of allowing work to proceed means you agreed to the contract.   Exactly what was the contract, we only have this bill.  So the court cannot rule otherwise, because any ruling has to be supported by evidence.

As for the oral agreement, your testimony is evidence, but if the contractor denies, his denial is also evidence, and it neutralized your testimoney, therefore the oral agreement cannot be proved. 

So the lesson is, get everything in writing.  The contractor is doing this trick every day, take it as a lesson.