This trip is possible from
Vancouver airport but you will have to take a ferry ride on the way to the Butchart Gardens. Fr om the airport you will need to drive twenty-five minutes Tsawwassen-Swartz Bay ferry where you will embark on a ninety-minute cruise through the Gulf Islands to Vancouver Island, BC.
When the Ferry finally arrives in Swartz Bay it is just a twenty-minute drive through the rustic and charming countryside to Gardens.
I hope this helped.