But many other Chinese Christians worship at so-called "underground" churches and say they face persecution or even physical abuse by communist authorities.
According to the Chinese constitution all Chinese are guarantied "freedom of religious belief", but rights groups say in reality the communist authorities fear any groups they cannot control or that could threaten their grip on power.
Estimates of the number of Christians in China vary greatly, but according to the government there are about 15 million practicing worshippers attending officially sanctioned churches.
Speaking ahead of his meeting with the Chinese president, Bush promised what he said would be "candid" talks, saying he would raise the issue of religious freedom and other human rights issues.
Bush and Hu last met a month ago at the G8 summit in Japan and no major announcements were expected from Sunday's meeting.
"I enjoy our conversations... our relationship is constructive and it's important and also very candid," Bush told reporters ahead of the talks.
|Chinese are officially only allowed to worship at state-sanctioned churches [GALLO/GETTY]
"I feel very strongly about religion," he added, calling the church visit a "spirit-filled feeling".
Bush has been criticised by human rights activists and by senior US politicians for not using he visit to China to speak out more forcefully on rights issues.
But he has insisted he can make more progress by candid, behind-the-scenes dialogue with Chinese leaders.
Last week Bush used a speech in the Thai capital, Bangkok, to express "deep concerns" over China's human rights record, saying China would not realise its full potential without respect for human rights.
"America stands in firm opposition to China's detention of political dissidents and human rights advocates and religious activists," he said.
Inside China however, Bush has taken a much more delicate diplomatic line, aware that China's leaders view the Olympics as their moment in the spotlight and their insistence that the games should not be used as a political platform.
Commenting on his visit to a Beijing church Bush said his attendance at Sunday's worship had been "a very uplifting experience" and thanked Hu, the Chinese president, for helping to arrange the visit.
The service was conducted almost entirely in Chinese, but was specially translated for the US president and his wife, Laura.
For his part Hu, who spoke first, focused his remarks to reporters on the Olympics; offering his congratulations at US swimmer Michael Phelps's gold medal win on Sunday.
Thanking Bush for making his fourth trip to China, the most by a sitting US president, Hu said the visit was "a true testament to the importance you place on relations with China".