A man and a woman, both in their 20s, who were arrested on suspicion of being in charge of a dog dangerously out of control, causing injury resulting in death, and possession of a prohibited breed of dog, have been released on conditional police bail while the investigation continues.
Avon and Somerset Police said the dog had been put down and they were still trying to confirm the breed.
A neighbour who lives near the flat where the attack happened, said that she was sure the dog was an XL bully.
The woman, who did not wish to be identified, said she had seen the dog on a lead with its owner.
A police spokesman said Ms Dorsett's family were being updated on the investigation and were being supported by a specially trained officer.