The incident happened around 11am after the man followed the victim from the car park before exposing himself.
It was later reported by a member of the Black Tom Prime Ministers residents’ group on Facebook who wanted to alert others visiting the park.
The post stated: “Please be aware of a very unpleasant incident in Bedford Park which Police are aware of.
" A lady I know was walking her dog and a man of about 20 followed her from the car park before exposing himself. She screamed at him and sadly two other men nearby did nothing to help or support her. Even more worrying was that he had tailed her for a while through the park first.
"Please be aware and alert, even in broad daylight.”
A Beds Police spokesman confirmed the force is looking into the incident.
"We were called to reports of an indecent exposure by a man in Bedford Park yesterday (11/5) at around 11am,” the spokesman told The Beds Times and Citizen.
“Officers attended the scene and carried out a search of the area, but no suspect was found.
“He is described as white, in his mid 20s and of slim build. He was wearing a black sweatshirt, black jogging bottoms with a white stripe down them, and black trainers.”
Anyone with information is asked to get in touch by calling 101 or via the online reporting tool. Please quote reference 153 of yesterday.