A 15-year-old boy, who said he escaped from the bus, said: "All my colleagues were shot, we don't know where the bullets came from."
He said: "I survived and some of my colleagues, around five or six people. All the others were lying on the ground, I don't know if they were killed or wounded."
An interior ministry source confirmed there was an attack on a bus in the Amriya area.
He said initial reports were of four dead and nine wounded, but that the toll could rise.
Violence
Hundreds of people are killed every week in attacks in Iraq and buses carrying workers have frequently been targeted by kidnappers and armed men.
Security sources say the main road to the airport, which also houses the main US military base in Baghdad, has seen a rise in attacks in recent days.
The transport ministry, which controls the airport, is run by supporters of Muqtada al-Sadr, the Shia leader, whose al-Mahdi Army has been accused by Washington and Sunni Arabs of operating death squads.
The attack comes after Nuri al-Maliki, the Iraqi prime minister, promised a security crackdown in Baghdad that would crush armed groups "regardless of sect or politics".
The hanging of Saddam Hussein at the end of 2006 and the release of an illicitly filmed video showing the former president being taunted on the gallows, possibly by followers of al-Sadr, has heightened tensions in Iraq.