Probably go on worshipping just as before. Just because we discovered His bones does not mean that He still did not rise from the dead and that He still did not work miracles and that we have thousands of Saints who have worked miracles and attest it to Him. I would however though feel that our entire Christology would be shattered considering that I would find it strange and heretical that only His soul resurrected and not His body, because we have been taught that soul and body will be resurrected and that Jesus redeemed the physical world. Other than that, I'd stay Orthodox.
It may also be fair to mention that if something like this were to actually happen, I would be very skeptical about it and chances are there would at least be enough room for reasonable doubt. I mean, really, how are we going to identify the bones of a man who lived 2,000 years ago without even any DNA to go from? Remember, He never had any children, his half-brothers or cousins were from His father's side whom He really had no genetic relationship.The only way a theory like this would even have a hint of potential validity would be if they could prove that the bones are somehow genetically related to the Theotokos. But even then, how would we have her DNA and just because their DNA is related, is it enough to confirm that the bones are of Jesus? What if it was just one of her distant cousins or siblings or something? Chances are if a theory like this ever did come forward, it would be based off of some heresy or conspiracy theory that is unsupported by evidence, therefore the whole argument would come falling down.