and another 11 people died in a blast at a city hospital around 90 minutes later.
The second attack hit the emergency ward of the city's Bolan Medical Complex where the wounded were taken and was followed by a gun battle with militants holed up inside the hospital.
The standoff lasted for several hours and ended when security forces stormed the building, freeing 35 people who had been taken hostage, Interior Minister Chaudhry Nisar told reporters.
Quetta was the scene of two of the bloodiest attacks in Pakistan this year, both targeting Shiite Muslims, and the student victims were members of a women's university popular with the minority community.
Nisar said the bus bomb killed 14 students and wounded 19.
"As casualties were being brought to the hospital terrorists had taken position inside the hospital building," he told reporters.
"They opened fire on administration and police officials who arrived at the hospital. One suicide bomber blew himself up in the hospital."
Nisar said he was unable to give exact casualty figures for the hospital attack, but Abdul Wasey, spokesman for the paramilitary Frontier Corps earlier said 11 were killed and 17 wounded in the bombing.
No group has yet claimed responsibility for the attacks but Quetta is a focal point for sectarian violence between majority Sunni Muslims and minority Shiites, who account for 20 percent of Pakistan's 180 million population.
A giant bomb planted in a water tanker being towed by a tractor killed 90 Shiite Hazaras in February, while another suicide bombing at a snooker club in January killed 92 others.
Lashkar-e-Jhangvi, a militant group officially banned by the government in 2002, claimed responsibility for both attacks.
The bus targeted in Saturday's attack was from Sardar Bahadur Khan Women's University, which is located close to a Shiite Hazara neighbourhood in Quetta, and many Hazaras are students.
Baluchistan, which borders Iran and Afghanistan, is rife with Islamist militancy and a regional insurgency waged by separatists demanding political autonomy and a greater share of profits from the region's natural resources
Overnight, separatist militants blew up a historic building in Baluchistan linked to Pakistan's founding father, razing its structure to the ground.
The attackers armed with automatic weapons entered the 19th century wooden Ziarat Residency after midnight and planted several bombs, senior administration official Nadeem Tahir told AFP.
Mohammad Ali Jinnah, the driving force behind the creation of the Pakistan, spent his last days in the building which was declared a national monument following his death, one year after the country's independence in 1947.
The building is in Ziarat town, 80 kilometres (50 miles) southeast of Quetta.
"They shot dead the guard who resisted the intruders," Tahir said.
Police official Asghar Ali said militants planted several bombs and detonated them by remote control, completely gutting the building.
At least four blasts were heard in the town, he said. The building caught fire and it took five hours to bring the blaze under control as Ziarat, a small hill station, has no fire brigade.
A separatist-group later claimed responsibility for the attack.
"We blew up the Ziarat Residency," Meerak Baluch, a spokesman for the Baluchistan Liberation Army told AFP in a phone call from an undisclosed location. "We don't recognise any Pakistani monument."
Pakistan's new Prime Minister Nawaz Sharif appointed Baluch nationalist leaders as provincial governor and chief minister, raising hopes that some of the long-held grievances in the province about its treatment by the federal government could be addressed.