Heavy security prevented the bombers from getting into the Borno Express Terminal and the blast happened nearby at about 7:10 am (0610 GMT).
“The two terrorists approached the gate in their tricycle (motorised rickshaw) but could not have their way because of the heavy security presence,” said bus driver Mohammed Kabir.
“They hit an 18-seater bus that just went out of the terminus with passengers.”
Sama’ila Yusuf, a civilian vigilante assisting the military against Boko Haram, said the bombers turned away as all passengers were being screened before entry into the bus station.
“They hit a bus that just left the terminus on its way to Kano,” he added.
Reports indicated that the two victims were pedestrians. The two bombers were also killed.
There was no immediate claim of responsibility but the attack bore the hallmarks of Boko Haram, which has repeatedly hit bus stations, markets and places of worship with bombings and suicide attacks.
Peak period for travel into and out of the Borno Express Terminal is between 6:00 am and 11:00 am.
Maiduguri is the capital of Borno state, which has been worst affected by the six-year insurgency that has left at least 15,000 people dead and more than 1.5 million homeless.
Attacks have increased since Muhammadu Buhari became president on May 29. Nearly 570 people have died in that period, according to AFP reporting.
On Friday, Boko Haram gunmen shot dead eight people who returned to the abandoned town of Gamboru, on the border with Cameroon, to inspect their damaged homes.