"The future won't just be orange, it will be multi-coloured, multi-racial and people of all races, religions, backgrounds and sexual orientation need to live together and make a contribution," Ms Bernard said.
She was speaking at a Children in Scotland equality conference at Heriot-Watt University ahead of the deadline public bodies have been set to introduce positive race relations policies under the Race Relations Amendment Act 2000.
From next week, local authorities, schools and colleges must promote equality and good race relations - new duties that stem from the death of Stephen Lawrence, the young black Londoner who was stabbed to death at a bus stop.
Ms Bernard urged young Scots not to stand aside. "Do you want a Scotland where there is racism on the football terraces or where people die on the streets because of the colour of their skin or religious belief? Of course, you don't," she insisted.
She was victimised at school in London because of her Caribbean background. Her white friends could not always protect her and stood aside. "I would hope you would not do that in 2002," she said.
There were still difficulties securing a job if you were not white, although the country had moved on since her family were invited to Britain by the government more than 40 years ago. Her stepfather worked in a car factory, her mother in a hospital, despite problems in finding a house. "There would be signs saying 'no blacks, no dogs, no Irish' and that's changed a lot," Ms Bernard said.
Mark Batho, head of social justice in the Scottish Executive, urged young Scots to challenge their parents if they found them making racist remarks. Surveys had shown that one in four Scots admitted to being racist. "They are failing to set an example to young people of a Scotland that is multi-ethnic and prosperous," Mr Batho said.