The body of Karina Batista, 40, was discovered at a property in Kensington Park, Easton at about 10:20 GMT on Monday.
Murder detectives are asking for information to trace the movements of a red Peugeot 107.
A 36-year-old man has been arrested on suspicion of murder and remains in police custody.
A post-mortem examination found Ms Batista died from multiple injuries to the upper body.
A spokesman for Avon and Somerset Police said: "As part of our investigation we're keen to hear from anyone who saw the red Peugeot 107 between 3.15am and 6am on Monday.
"We believe the car, which has a hubcap missing from the front left wheel, was in the Keynsham area at the time."
A woman thought to have been murdered at a house in Bristol has been named by police.