The Chinese embassy in Bahrain only accepts visa application of Bahraini citizens and other citizens who work or reside in Bahrain for a long period.As you said, Your president is Saudi Arabia living in Al-khobar (a large city located in the Eastern Province of the Kingdom of Saudi Arabia on the Persian Gulf), so you can't obtain visa through Bahrain for him.

Aliens can also apply for Chinese Visa-on-Arrival on certain conditions. Please look through the website https://www.travelchinaguide.com/embassy/, there are detail information about it.