The bus stop is at the western highway entrance to Jerusalem, where crowds of commuters usually travel in the mornings.
According to an initial report from the health service, up to twelve people were injured, two of whom have life-threatening injuries.
It was later announced that one person had died from his injuries.
The second explosion occurred shortly afterwards in Ramot, north of Jerusalem.
Injuries are also reported from there.
Police and Israeli Prime Minister Benjamin Netanyahu describe the explosions as a synchronized attack.
All bomb dogs available will be used to ensure there are no more hidden explosive devices in the city, police chief Kobi Shabtai said, according to The Jerusalem Post.
The Israeli authorities have assumed early on that it would be a Palestinian attack, but the Palestinian authorities have not yet commented.
Tense year in the region
It has been a tense year in the region.
2022 is so far the deadliest year in the region since 2006. 19 Israelis have been killed in various acts and attacks by Palestinian perpetrators.
These attacks have escalated in recent weeks.
The Israeli military has carried out raids in the West Bank, leading to violence and killing many Palestinians.
During the year, more than 130 Palestinians have been killed.
Last Tuesday evening, Palestinian authorities announced that a 16-year-old had been shot dead by Israeli soldiers in the West Bank, in connection with an Israeli intervention in the city of Nablus.
According to Palestinian reports, a "large Israeli force" came to Nablus with a bulldozer in order to protect Israeli settlers.
The Israeli military has not commented on the events in Nablus.