The Syrian Observatory for Human Rights said at least 20 people were wounded in the explosion near Souq al-Hamadiyeh district, and that six of the dead were Lebanese citizens.
The Lebanese agency that organised their trip gave the same death toll.
Syrian state media, which reported a toll of six dead and 19 wounded, said the blast was caused by an explosive device rather than by a suicide bomber.
Officials had found and defused a second bomb that had been placed inside the bus before it detonated, said the official SANA news agency.
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Observatory director Rami Abdel Rahman said the bus was carrying Shiite Muslim pilgrims on a tour of religious sites.
In Beirut, an official with the Lebanese group that organised the trip said the passengers on the bus were Lebanese.
"They set out from Beirut at 5:30 am (0330 GMT) this morning," Fadi Khaireddin told AFP, adding that the bus had space for 52 pilgrims, as well as the driver and trip administrator.
"The bus is usually full," he added, though he could not confirm how many people were on the trip this weekend.
The agency had been making regular trips to Syria despite the civil war there, with groups leaving each weekend for a day-long visit to shrines revered by Shiites across the border.
Syrian state television showed footage from the scene of the blast, with men in military uniforms picking through the wreckage of the bus.
Its front half was mostly blown off, leaving only the metal frame, and bags of belongings were strewn across the remaining seats.
The Lebanese Shiite movement Hezbollah denounced the attack.