Anna Lewis, 27, who lives in Fishponds, was last seen at a work placement in Southmead on Friday, 14 April.
She was reported missing to police on Friday by her family, who do not live locally.
Avon and Somerset Police said it is growing increasingly concerned for her well-being.
The disappearance of a woman in Bristol who has not been seen for more than a week has been described as "out of character".