The provincial security chief accused local Taliban of planting the bomb and said the dead included women and children.
Fourteen others on the bus were injured, the Afghan news agency Khaama Press reported Friday.
Taliban militants attacked a checkpoint in northeastern Afghanistan Thursday, killing at least four police officers and injuring two others, police said.
The strike by the Taliban is the latest in a series of attacks in the Wardaj district of Badakhshan province, Khaama Press said.
Badakhshan provincial security chief Ghulam Sakhi Haidari denied a Taliban statement that said nine police officers were killed and the attackers had taken control of the checkpoint. He said the checkpoint remained in the hands of Afghan security forces.
In earlier attacks, at least eight Afghan police officers were killed in a Taliban ambush in the Kohi-e-Ghanio area of the district, and four of 16 kidnapped police officers were killed in the Bashin area, the Khaama Press report said.