Indonesia is the world's most populous Muslim nation and Yudhoyono is seen by the Bush administration as a key Asian ally in the war on terror.
However, many of Indonesia's 190 million Muslim are angry at American policy, particularly the wars in Iraq and Afghanistan, which have been portrayed as an attack on Islam.
In anticipation of protests hundreds of police and soldiers have been deployed in and around Bogor, manning checkpoints and checking vehicles entering the city.
There have been reports of death threats against the US president from Indonesian militant groups, and on Monday police said they were checking rumours that a suicide bomber might try to infiltrate the anti-Bush protests.
On Sunday, close to 13,000 people marched through Jakarta carrying banners reading "Bush: Wanted dead or alive for crimes against humanity" and dragging an effigy of the US president.
Protest organisers promised larger numbers when he flies in Monday.
Before flying to Indonesia, Bush toured Vietnam's financial capital, Ho Chin Minh City, meeting American and Vietnamese business leaders and exploring trade opportunities between the two former enemies.
"I am very interested in hearing what the opportunities are like and the obstacles you face. Perhaps the US can help foster the market economy that is growing here.
"When I read about the recent economic history of Vietnam, I am amazed at the size of growth and the fact that people are beginning to realise dreams," Bush said.
Bush was in Vietnam for the weekend summit of leaders from the 21-member Asia-Pacific Econimic Co-operation (Apec) forum.
The visit was only the second by a US president since the end of the Vietnam war.