Anna Lewis, 27, who lives in Fishponds, was last seen leaving Southmead Hospital on 13 April.
Avon and Somerset Police said they were increasingly concerned for her welfare and specialist teams were searching in north and central Bristol.
Ms Lewis is described as white, about 5ft 5in tall, of slim build, with brown eyes and long dark brown hair.
Det Insp Roger Doxsey, who confirmed foul play was not currently suspected in the case, thanked the public for their support and said all potential sightings are being followed up.
He said officers are concentrating on remote outdoor areas as Ms Lewis, who tends to wear her hair in a low ponytail, was known to go on camping trips.
She often wears jeans or walking trousers, hiking boots and loose jumpers.
Ms Lewis was reported missing on Friday by her family, who do not live locally.
Det Insp Doxsey said: "We are supporting Anna's parents and are keeping them fully updated on our inquiry as it progresses.
"We're also working with UWE Bristol and Southmead Hospital to try and find out as much as we can about Anna and her movements in the days before she went missing."
A trainee nurse who went missing from Bristol has been reportedly seen 10 times since a search for her began.