"I believe that most Japanese and Chinese visitors understand that shaking hands is
a western 'ritual' and originally out politeness and now, perhaps because many in the East have assimilated this custom, it may way be considered impolite not to bow AND shake hands."
I think that this is a good point. Right now, I am attending a university, where there are about 25% Japanese students--not to mention a number of Chinese and Taiwanese students. However, where I am majoring in Japanese, I have been encouraged by my professors to learn more about the culture from my Japanese friends.
Due to my prior knowledge of the culture I had attained through my martial arts training, the professors took time with me, and made sure I knew how to behave appropriately in an office setting. Bowing is a very big part of this, both from the boss to the worker, or the teacher to the student--similar to in the dojo. However, due to my interest, I have also been given opportunities to participate in interculural activities--between Japanese and Americans. Although my experience is still limited, I have found that at such functions, it seems to be customary to first bow, and then a hand shake may follow, depending on the circumstances. In some cases, it seems that that Japanese expect that if the American has a good understanding of the culture that the bow is sufficient, but a handshake may also be extended, not purely as ritual, but more of a willingness to build a bridge between the two culures.
I think that the majority of Japanese probably have no problem at all with shaking hands (no religious issues anyway), but when it comes to a choice, the bow is still the main preference (for obvious reasons), although that may be changing for the younger generation, as many things are. You mentioned the point of assimilation, and I think that is especially evident in the younger generation.
So, bowing is still an extremely important part of Japanese culure, the back bone of etiquette. It's where everything from simple greetings to business gatherings start and end. And I think that many Japanese feel (especially the older generation) that if an American--or any other culture--wishes to attain a thourough understanding of the Japanese culture, he must understand the bow--not only inside the dojo, but also inside Japan.