The bus was passing in front of a hospital in a residential district of Turkey's largest city when the blast occurred on Thursday, media reports said.
Istanbul Governor Muammer Guler told reporters the bomber in the commercial capital of Istanbul was an unidentified woman carrying the device in her lap when it exploded on board a bus outside a hospital in the mainly residential Fatih district.
"The bus was not the target. The bomb was being carried from one place to another ... We suspect a Marxist-Leninist group."
The blast killed three people immediately, including the bomber, and injured 15, said surgeon Korhan Taviloglu at the hospital treating casualties. A woman died later in hospital.
Police detained three suspects in connection with the bus explosion, Anatolian news agency said, adding a female suspect was believed to have been on the bus when the explosion hit.
Only hours earlier, a small bomb exploded outside the hotel in Ankara where US President George Bush is expected to stay on Saturday night during a visit to the Turkish capital.
Two people, including a Turkish police officer, were injured in the blast, reportedly caused by a parcel bomb.
All the protests against the NATO
conference have been peaceful
The device was hidden in a package at the entrance to the Hilton hotel car park, an ambulance official said.
The policeman was inspecting a booby-trapped parcel when it blew up about 20 metres from the entrance to the hotel, witnesses said.
Local residents had called the police after spotting a suspicious package.
The policeman lost a leg, the ambulance official said. A second policeman is reported to have suffered facial injuries.
The blast also damaged a nearby car and broke windows of neighbouring buildings.
A small Marxist group, MLKP-FESK, claimed responsibility for the Ankara blast, private NTV television reported. Police would not comment on the report.
Bush is due to arrive in the Turkish capital late on Saturday for talks with Turkish officials on Sunday before travelling on to the country's largest city, Istanbul, for the two-day NATO summit which starts on Monday.
British Prime Minister Tony Blair, French President Jacques Chirac and other alliance leaders are also scheduled to attend the summit.
Turkish Deputy Prime Minister Mehmet Ali Sahin said security measures would be heightened after the blast. Turkish media had been reporting that 7000 police officers would be on duty in the capital for the Bush visit.
"Measures will be increased from now on," Sahin said.
Turkish security forces are using concrete barriers to seal off a zone in the heart of the city and surveillance aircraft are being prepared to help monitor a no-fly zone over the area.
Concerns about security have grown in Turkey since last November, when four truck bombings killed more than 60 people in attacks on two synagogues, the British consulate and a London-based bank.