The witness is a woman seen pushing a pram on the morning of Friday 27 January, when Ms Bulley went missing.
“It is believed that the female in question may have walked along the river path during these times and so detectives want to speak to her and urge her to get in touch,” Lancashire police said.
Lancashire Police said the woman was seen walking from the direction of Allotment Lane towards the Grapes public house at approximately 8.22am and is seen again walking on Allotment Lane towards Garstang Road at 8.41am.
It is believed that the female in question may have walked along the river path during these times, police said.
The force added: “We are also appealing to anyone who was driving down Blackpool Lane/Garstang Lane on the morning of Friday 27th January between the times of 9am and 10am who has dash cam footage on their vehicles to make contact.”
The appeal comes after family and friends have questioned a police theory that the missing dog walker fell in a river.
In a Facebook post, Ms Bulley's sister, Louise Cunningham, urged people to “keep an open mind” as there is “no evidence whatsoever” that the dog walker fell in the river.
“Off the back of the latest Police media update, please can I add there is no evidence whatsoever.
“Everyone needs to keep an open mind as not all CCTV and leads have been investigated fully, the police confirmed the case is far from over.”
Search teams from Lancashire Constabulary are continuing to trawl the River Wyre near St Michael's, working on the hypothesis that the missing mother-of-two, from nearby Inskip, could have fallen in when she disappeared on 27 January.
Ms Bulley’s friend, Emma White, also cast doubt on the police theory, telling Sky News it was based on “limited information”.
“When we are talking about a life we can't base it on a hypothesis - surely we need this factual evidence,” she said.
Police believe the 45-year-old mortgage adviser went missing in just "a 10-minute window" while she was walking her dog, Willow, close to the River Wyre, after dropping off her daughters - aged six and nine - at school.
Ms Bulley had logged in to a Microsoft Teams call at 9.01am, which ended at 9.30am with her phone still connected to the call.
She was seen by another dog walker at 9.10am - the last known sighting - and police traced telephony records of her mobile phone as it remained on a bench overlooking the river at 9.20am.
The device was found by a dog walker at around 9.35am, with Willow nearby.
The police search has been aided by specialists and divers from HM Coastguard, mountain rescue, and Lancashire Fire and Rescue Service - with sniffer dogs, drones and police helicopters deployed.
Detectives are also working behind the scenes to analyse CCTV and dashcam videos, and members of the public with footage which could be useful have been urged to come forward.