Bowing in Buddhism is a sign of respect and gratitude. We frequently bow three times, to the Three Treasures, or nine times, to all three in past, present, and future. Bowing 108 times for remembering all of the entrances of delusionis less common. We bow to Buddha Nature, not to selves, starting by respecting ourselves.
Bowing in Chinese culture is a sign of submission of the inferior to the superior. Thus the official Qing dynasty history says that the first British ambassador to China, George Macartney, 1st Earl Macartney, bowed to the Qianlong Emperor with his head on the floor (kowtow), and the official British Imperial history says he didn’t. This is about self, and thus is nothing to do with Buddhism.
As long as bowing continues, Buddhism will last.
Dogen Zenji
Buddha recognizes Buddha; Buddha bows to Buddha
Jukai Ceremony
At some monasteries we lead the lay people taking the precepts at Jukai onto the altar, and all of the monks bow to them as baby Buddhas. I’m sorry I don’t have any photos of this version of the ceremony, but we do have this.
There are many kinds of Buddhism, but they all agree on bowing.
A South Korean Buddhist monk bows toward the U.S. embassy during a rally demanding quick recovery of U.S. Ambassador Mark Lippert in Seoul, South Korea, Friday, March 6, 2015. A knife attack on Thursday that injured Lippert is the latest act of political violence in a deeply divided country where some protesters portray their causes as matters of life and death. The attack, which prompted rival North Korea to gloat about "knife slashes of justice," left deep gashes and damaged tendons and nerves. The banners read: "A rally demanding quick recovery of U.S. Ambassador to South Korea Mark Lippert.
The Power of Prostration