It is not permissible to bow to anyone when greeting them, whether in the context of sports or otherwise. The Prophet (blessings and peace of Allaah be upon him) forbade that.
Al-Tirmidhi (2728) narrated that Anas ibn Maalik (may Allaah be pleased with him) said: A man said: O Messenger of Allaah, when one of us meets his brother or friend, should he bow to him? He said: “No.” He said: Should he embrace him and kiss him? He said: “No.” He said: Should he shake hands with him? He said: “Yes.” Classed as hasan by al-Albaani in Saheeh al-Tirmidhi.
Al-Mubaarakfoori said in Tuhfat al-Ahwadhi:
Bowing means tilting or inclining the head and back.
“He said: ‘No’” because it is the same as rukoo’ (bowing), which like sujood (prostration) is an act of worship before Allaah, may He be glorified.
“Should he embrace him” i.e., hug him and clasp him to himself, “and kiss him. He said: ‘No.’” End quote.
The scholars of the Standing Committee for Issuing Fatwas were asked: We joined a karate club in America and the trainer said that you have to bow when he bows to you. We refused and explained to him that this is against our religion, and he accepted that but he said that we should tilt our heads only, because he is the one who bows first and it is essential to return his greeting. What is your opinion on that?
They replied: It is not permissible to bow in greeting to a Muslim or to a kaafir, whether that involves the upper part of the body or the head, because bowing is a kind of worship, and worship is only for Allaah alone.
And Allaah is the source of strength. May Allaah sent blessings and peace upon our Prophet Muhammad and his family and Companions.
Shaykh ‘Abd al-‘Azeez ibn ‘Abd-Allaah ibn Baaz, Shaykh ‘Abd al-Razzaaq ‘Afeefu, Shaykh ‘Abd-Allaah ibn Ghadyaan, Shaykh ‘Abd-Allaah ibn Qa’ood