Burgess took up archery in 1998 and made her international debut in 2001. As a teenager Burgess was widely regarded as an upcoming star of British archery, narrowly missing out on qualifying for a spot at the 2004 Summer Olympics in Athens, aged just 17. In 2007 Burgess won a bronze medal for Great Britain with Alison Williamson and Naomi Folkard in the women's team event at the 2007 World Archery Championships, defeating the Italian team in the bronze medal match following a defeat to South Korea in the semi-final. Later that year Burgess, Williamson and Folkard were medallists at the fourth stage of the 2007 Archery World Cup held in Dover, winning the women's team recurve tournament. This was however not enough for Great Britain to advance to the final. Burgess, Folkard and Williamson improved on their medal tally in the 2008 Archery World Cup, winning a gold medal in the team competition in Santo Domingo, Dominican Republic, in April, and a bronze medal in the same event in Boé, France, two months later.
Burgess qualified to represent Great Britain at the 2008 Olympics, competing in the team and individual events. Once again partnered by Alison Williamson and Naomi Folkard, she helped Great Britain achieve a surprise second place in the team ranking round. In the quarter-finals the trio overcame the Japanese team by five points to meet hosts China in the semi-finals. Burgess and her teammates were unable to defeat the Chinese team, missing the opportunity to compete for the gold medal. They instead faced France in the bronze medal match, but lost to their French opponents, having to settle for fourth place overall. In the individual event Burgess placed 40th out of 64 archers in the ranking round. She defeated China's Guo Dan in the first round before falling to teammate Folkard in the second round.
On 11 January 2008 Burgess and her boyfriend - fellow archer Roy Nash - were attacked by a group of teenagers outside an indoor archery range in Cheadle, near Stockport, Great Manchester. They were treated for their injuries at Stepping Hill hospital, both suffering bruising to the face. Despite this Burgess managed to qualify for the European Indoor Championships in Turin just two days later.
