More than 30 people were also injured when the bus exploded at Burgas airport, by the Black Sea.
Witnesses told Israeli TV that someone boarded the bus and a huge explosion immediately followed.
Israeli Prime Minister Benjamin Netanyahu later accused Iran of being behind the explosion.
“All the signs lead to Iran,” he said in a statement.
“Israel will respond forcefully to Iranian terror.”
The Israeli foreign ministry said in a statement: “There are six bodies on the scene – one critically wounded died at the hospital and two seriously injured are in intensive care. Thirty more people are being treated.”
It said the bus was carrying tourists from a charter flight that arrived from Israel.
Wednesday’s blast came on the 18th anniversary of a deadly attack on a Jewish community centre in Argentina. Israel blamed Iran for that attack – a claim denied by Tehran.
Israeli officials said passengers from a Tel Aviv-Burgas flight boarded the bus shortly after 17:00 local time.
“We don’t know if it was a terror attack. We do know it was an explosion,” Israeli Foreign Ministry spokesman Paul Hirschson was quoted as saying by the Associated Press news agency.
Two buses standing nearby were also damaged.
“I arrived at the airport about half-an-hour after the explosion, and saw three buses completely burnt out – just the metal bars were left,” Bulgarian journalist Dobromir Dovkacharov said.
“There were crowds of people around, very distressed. One man said he saw decapitated heads. Others spoke of body parts flying through the air,” he added.
More than 40 people are reported to have been on the bus. Local officials say the death toll could rise further.
Burgas airport has now been closed and flights are being diverted to Varna.
In January there were reports that Israel had asked Bulgaria to tighten security for Israeli tourists travelling by bus.
This followed a reported discovery of a suspicious package found on a bus with Israeli tourists travelling from Turkey to Bulgaria.
Israeli tourists have been targeted in attacks in a number of countries around the world.
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