As a junior, Bismpikou enjoyed a successful career on the European competitive circuit. She made her major senior Gymnastics debut at the 2003 World Championships in Anaheim, California, where she qualified to the Olympics with a score of 34.637. In early 2004, she had a strong showing at the European Championships, placing 12th in the all-around final. Bismpikou represented her country in her hometown of Athens at the 2004 Summer Olympics. There she advanced to the individual all-around where she finished a respectable 15th with a final score of 36.499, almost two full points higher than her World Championships score the year before.