Naomi Waite, 30, visited the park on Saturday, March 19 with her 2-year-old son, and other family members – including her 8-year-old sister.
At around 4pm, she was sitting on the grass with her son, when she saw men riding off-road motorbikes on the footpath.
She said: “They then came shooting up onto the field, probably at speeds of around 40 or 50 mph, heading directly for us.”
Mrs Waites shouted to her family, and they quickly sprung up to move out of the way.
After ensuring her family were safe, she phoned the police – while her 21-year-old sister took a video of the individuals.
Mrs Waites said the bikers then started to perform tricks – ruining the pitch in the process – before driving off.
While no-one was injured in the incident, Mrs Waites said: “In my eyes, it is not going to take long before something really terrible happens.”
On the day in question, she said the park was full of families with young children, dogs and cyclists.
She added: "I feel like it was a purposeful intimidation. They were choosing the time where it was going to be most busy to get the biggest reaction.”
Since then, Mrs Waites has not visited the park as often as she usually would.
"It’s infuriating, because it’s the most wonderful place to go, especially with children”, she said.
"Sadly, it just doesn’t feel like a safe place to go.”
She continued: "For me, having a child, imagining the worst case scenario is just hideous.
“There’s no way they could stop if a child was in front of them.”
Police recently launched Operation Pillar to tackle anti social behaviour in the South-West of Edinburgh. However, Councillor Ashley Graczyk commented on the operation, and said: “More robust action from the Police is needed”.
Mrs Waite has not heard from the police since the incident, which she said she found “quite disappointing”.
Inspector Keith Forrester, of Wester Hailes Police Station, confirmed that police had received a report of males on motorbikes riding on paths and grass within Saughton Park.
He said: “Officers attended immediately however only one rider was observed and he made off upon seeing police.
“We are very aware of recent reports of antisocial use of off-road bikes at various locations across Edinburgh, including Sighthill Park and Saughton Park.
"Operation Pillar was introduced to deal with this issue and has seen additional patrols, including officers on police off-road bikes, being deployed to prevent further incidents, which cause fear and alarm to members of the public within the public parks. These patrols will continue as tackling antisocial behaviour is a priority for the South West policing team.
"We are also working with City of Edinburgh Council colleagues to capture CCTV footage of the bikers to identify those involved.
“If anyone has any information regarding the use of off-road motorcycles, I would encourage them to contact Police Scotland via '101'. Please provide as much information as possible so we can act to further reduce the antisocial use of these vehicles, thank you.”