The attack happened in the Old City early on Sunday, when the bus was waiting at a parking lot.
The seriously injured are said to be a pregnant woman who was hit in the abdomen and a man with injuries to, among other things, the head.
The police have cordoned off the crime scene and are looking for two perpetrators who fled the scene.
The attack comes after a tense week between Israelis and Palestinians, which followed three days of fighting between Israel and terrorist-branded Islamic Jihad that ended with a truce on Sunday night.