It is true that Chinese and Japanese culture shared a lot of things in common, but the two countries' history walked two very different path after Tang dynasty.
For one Japan had never been invaded by a foreign power. By invasion I mean foreign power marched down on your territory, completely destroyed your defense, and bring forth a new culture. China experienced this twice: one during Mongol (Yuan dynasty) invasion, second during Manchu (Qing dynasty) invasion. While Han culture had survived these two invasion, it survived not by upholding its tradition, but rather by absorbing new customs and morphed into something new.
Japanese style bowing was a traditional Han greeting gesture. People bow to each other with their hands holding together and reaching forward.
Later during Manchu rule, people had follow the Manchu tradition of “打千" (for men) and “万福” (for women)
(can't find a better picture, but you get the basic pose for men)
But I think the definitive reason that we don't bow to each other anymore is because we had went through communist rule that almost completely westernized Chinese society. Old traditions were despised and threw away. We replaced bowing with hand shaking. It's not a slow culture/custom change, it's a brutal and forceful cut that severs the old from the new. You're considered uncivilized and outdated if you bow while other people try to shake hands with you.
Japan never had this. Their westernization is an addition, not a replacement. They didn't give up their old ways, they just add the new ways as a more fashionable alternative. At least that's how I understand their Meiji Restoration.
We can't stop modernization (which in most cases, means westernization), but if given the choice, I'd rather have it like Japan, instead what we had after 1949.