"The bomb was planted in a television set and we successfully defused it," Ghulam Nabi Memon, a senior police officer, said.
Shias in Pakistan are marking Arbaeen - the end of a 40-day mourning period for Imam Hussein, a grandson of the Prophet Muhammad who was killed in a seventh century battle in Karbala.
The violence in Karachi echoed similar attacks in Iraqagainst Shia Muslims gathered in Karbala to mark the occasion.
It was not clear if either attack was carried out by a suicide bomber.
"A bomb was planted on the motorcycle and it hit the bus," Waseem Ahmad, the city police chief, said.
"We cannot determine in one and a half hours whether it was a suicide blast or not. We are examining the site. We are collecting the evidence. We are taking witness statements and then we will say something concrete."
Kamal Hyder, Al Jazeera's correspondent in Islamabad, said that it was unclear who had carried out the two attacks on Friday, but he noted that the city had previously seen ethnic, sectarian and political violence.
"It would appear that whoever is conducting these acts of terror in Karachi wants to destabilise Karachi," he said.
|The first explosion hit a bus carrying
Shia worshippers [AFP]
"There has been a lot of talk that Karachi is a strategic city, it is a port city, but whoever wants to hit Karachi primarily wants to do so because it is the financial heart of the country.
"Karachi has also seen an unrelenting wave of firing incidents, snipers shooting at ordinary people across the city."
The Pakistani Taliban have claimed past attacks against Shia Muslims in Pakistan.
Two attacks in Karachi last Decemberclaimed by the Tehrik-e-Taliban Pakistan left at least 60 people dead and unleashed a wave of angeron the city's streets.
Pakistan had tightened security in the city to protect mass processions of worshippers during Ashoura- deploying tens of thousands of police and paramilitary forces.