The fatalities happened when a fire broke out following the head-on crash in the region of Ancash, some 370 kilometers (230 miles) north of Lima, public prosecutor Edwin Ramos told RPP radio station, AP reported.
Police in Casma province said the bodies were burned beyond recognition and coroners will use fingerprints to identify the dead.
The motorcycle taxi driver was among the victims, while police detained the bus driver.
Six people were also injured and transferred to the regional hospital in Casma.
Some 50 people were aboard the bus, which was traveling to Lima from the northern region of Piura.
Road accidents are common in Peru where speeding, the poor state of roads, a lack of road signs and little control from authorities are contributing factors.