Nakić-Bilić was one of the best European basketball players at the peak of her career, as evidenced by her three consecutive awards for the best female player in Europe (1988-1990). Playing with the Yugoslav national team from 1987 to 1990, she won three silver medals in three major competitions: the European Championship in Madrid (1987), the Olympic Games in Seoul (1988), and the World Championship in Kuala Lumpur (1990).
She spent most of her playing career with the Elemes club from Šibenik, with which she became the Yugoslav champion in 1991. That same year, she was also named the best athlete by the daily newspaper Sportske Novosti. She spent two seasons in Spain, playing for Symel Tenerife, and in 1995 she returned to Croatia and played for Zagreb's Croatia until the end of her career in 1999.
Currently, Nakić-Bilić serves as president of the Council for Women's Basketball at the Croatian Basketball Federation.
She will be inducted into the FIBA Hall of Fame alongside legendary basketball players such as American Reggie Miller and Serbian Predrag Stojaković. The list also includes China's Miao Lijie, Latvia's Skaidrīte Smildziņa-Budovska, New Zealand's Kirk Samuel Penney, and Romain Sato of the Central African Republic.