The word 'bonsai' is Japanese, but the art it describes started in China. Even today, the Japanese characters for bonsai remain the same as the Chinese. By the year 700 AD, the Chinese had started the art of 'pun-sai', using special techniques to grow small trees in shallow containers. This technique was later adopted by the Japanese, but it developed along slightly different lines due to the influence of Zen Buddhism and the fact that Japan is so much smaller than China and growing space so much more limited.
Bonsai were almost unheard of outside Asia for many centuries, it is only in relatively recent years that bonsai has spread to the rest of the world.