A Reuters camerman saw 20 bodies at the depot at Nyanyan bridge, around 8 km (5 miles) south of Abuja, and two witnesses said another 15 had already been removed by the emergency services.
"I was waiting to get on a bus when I heard a deafening explosion then smoke. People were running around in panic," said Mimi Daniels, who works in Abuja. Another blast followed, she said.
There was no immediate claim of responsibility but suspicion is likely to fall on Islamist militant group Boko Haram. The Islamists have been waging an increasingly bloody insurgency in the northeast.
Suspected Islamist militants killed at least 60 people in an attack on a village in northeast Nigeria late last week. Eight people were killed in a separate attack at a teacher training college, witnesses said.