In 2005–2006, her rookie bobsleigh season, Moyse and her partner Helen Upperton won the Canadian Championships and earned four medals on the World Cup circuit including a gold at an event in St. Moritz, Switzerland. Heather also set push start records on five international tracks. At the 2006 Winter Olympics, Moyse and Upperton finished in fourth place in the two-man bobsleigh event, missing bronze by five one-hundredths of a second behind the host Italian team. The pair set the push start record for the Olympic track with a 5.16-second start time in their first heat.