Since I started to practice Bugei, I've seen so many foreign students who visit to Japan. Most of them study Bugei very honestly.
I believe you already to know that the studying politeness in Bugei is one of the most important factor.
I would like to talk about this for a while.
The origin of the word "politeness" came from "politus" Latin.
It is meaning "smooth".
In short, this word is pointing the smoothness in the society. The smoothness for between human and human. I can say it is symbolized by shaking hands.
On the other hand, the origin of the word "禮(礼)" came from the shape of the votive for god or Nature. When we dedicate the votive, Japanese act for it with care. It is not for the human society. I can say it is symbolized by bow.
As you guessing, shaking hands is designed for only human society. You can shake the hand with other single human. But you can't do so with any nature phenomenon, objects and animals.
But bow can express thanks to all of things including human also at the same time. That is the most remarkable difference between bow and shaking hands. I can affirm that that is the way of the Japanese thinking.
Of course, we understand that showing politeness to non-human is very strange custom for foreigners. But I have to say that is Japanese.
If you are trying to study something Japanese traditional arts, following this deed is most helpful for your understanding of Japan.
After that, you may feel the connection between all of nature and god. That is the sense of Japanese.
It is very nice video for understanding "bow"
A Bugeisha, Fudoan Hekishusai