At least 29 people have been killed in the blasts, a Red Cross official told the Reuters news agency.
Earlier in the day, suicide bombers killed at least 11 people in neighbouring Cameroon.
At least 49 people were killed in blasts at a market in Gombe last week. That attack was blamed on Boko Haram militants.
The Islamist group, which often targets northern Nigeria, has stepped up attacks since President Muhammudu Buhari took office in May.
No group has said it is behind Wednesday evening's attacks, although Boko Haram has targeted bus stations in the city before.
It is feared that the Gombe death toll will rise with reports of dozens of people injured.
One witness told the AFP news agency that he had counted 30 dead bodies at one of the bus stations.
Last year, Boko Haram took control of a large area of north-eastern Nigeria and declared a caliphate (a state governed in accordance with Islamic law).
Nigeria's military, backed by troops from neighbouring countries, including Cameroon, has recaptured most of the territory, but in recent weeks there has been an upsurge in suicide attacks.
Hours before the attack in Gombe, suicide bombers targeted Maroua in northern Cameroon. The attack left at least 11 people dead and injured dozens more.
A local source told AFP news agency the bombers were two young girls who had disguised themselves as beggars.
One of the bombers detonated the explosives at the city's central market, in what is the second such attack in the past week.
The authorities have now extended a ban on wearing burkas to include the commercial capital Douala.
Previously the ban had only been in place in the country's Far North region, after two suicide bomb attacks there earlier this month.
The Cameroonian army uses the town of Maroua as the headquarters for its operations against Boko Haram, as part of a multinational force battling the militants in neighbouring parts of Nigeria.
President Paul Biya has described the attacks as "cowardly and ignoble".
According to Amnesty International, at least 17,000 people, mostly civilians, have been killed since Boko Haram launched its uprising in 2009.
The group is still holding many women, girls and children captive, including 219 schoolgirls it kidnapped from a school in Chibok in April last year.
Reports from Nigeria say at least two bombs have ripped through two bus stations in the northern city of Gombe.