Officers discovered the the woman at the stop in a neighbourhood in the north of Bern at 2am, cantonal police said.
Police earlier received a call that a woman on Winkelriedstrasse needed help.
When officers arrived at the bus stop in front of St. Mark’s church they found the woman badly injured, police said.
Despite efforts to resuscitate her, police could only determine that the victim was dead.
Police said the woman, who has not been formally identified and whose age was not disclosed, was “the victim of a violent crime”.
From initial findings it appears that the perpetrator knew the woman and that he fled after attacking her, police said.
Police closed a section of Winkelriedstrasse for five hours while examining the crime scene.
A tracking team using a dog searched the area.
Police for the moment are not issuing further information.
The regional prosecutor for Bern-Mitelland has launched an investigation into the homicide.