The attack in Ramadi, the capital of mainly Sunni Anbar province and a former al-Qaeda stronghold, raised fears of renewed sectarian violence.
The bus, carrying 45 Lebanese pilgrims, was heading to Baghdad from Syria, the source said.
"A roadside bomb exploded near a bus carrying Lebanese pilgrims coming to Iraq, probably to visit the sacred shrines in Iraq," said the source, speaking on condition of anonymity.
Violence has eased in Iraq since the height of the war in 2006 to 2007 when tens of thousands were killed as Sunni and Shi'ite militants fought one another.
But Sunni militants linked to al Qaeda remain a potent force, and often attack security forces and Shi'ite targets in an attempt to stir up sectarian tensions.