The bombings, which occurred near a hotel and a military headquarters, came a day after a suicide bombing in a neighboring region killed 43.
A security official in the Bouira area told the Associated Press that nearly all the victims were civilians.
Wednesday's first bomb targeted a regional military command and injured four soldiers, the state-run APS news agency said.
"Parts of the walls have fallen off, the fence is destroyed, cars are buried under the rubble," Abdellah Debbache, the Bouira correspondent of Algeria's Liberte newspaper, told the AP by telephone.
Halim Osbani, who lives near the military barracks, told Reuters that a suicide bomber rammed a car into the building.
"The blast pulverized the bomber's body into pieces, with bits of his limbs strewn meters away," Osbani said.
Minutes later, 11 people died and 27 were wounded when a second bomb went off next to a downtown hotel, exploding just as a bus passed by carrying workers to a dam construction site, APS and state-run radio said. Most of those who died were traveling on the bus.
"The bus was left a complete wreck," one witness told Reuters. "Nearby were pools of blood, watches, tattered clothes and a mobile telephone still ringing."
Bouira is part of a so-called "zone of death" it forms with Algiers, Tizi Ouzou and Boumerdes where attacks have been rife.
No one has claimed responsibility for the bombings Wednesday or the five other attacks this month. All have occurred in the area east of the capital of Algiers where militants from an offshoot of al-Qaida are suspected to operate.
On Tuesday, a suicide bomber drove a car packed with explosives into the entrance of a police school killing 43 people and injuring 45 in Issers, also east of Algiers.
It was the deadliest attack this year in Algeria and worse than the December attacks in Algiers against government and United Nations buildings, which killed 41 people and injured many others.