Baško first played in a professional team in 1995.[1] After three years with the local RTU/Klondaika Rīga team Baško moved to Siena Saints of NCAA.[1] In 2003, she moved to Israel, then spent four years in France and is currently a member of Wisła Can Pack Kraków team.[1]
At age 19, she already represented Latvia at EuroBasket Women 1999. She was one of the youngest players in the tournament.[1] Baško also contributed to the successes of the team in EuroBaskets2005 and 2007.[1]
In August 2011 Gunta Baško married ex-basketball player Kristaps Melnbārdis, and changed surname form Baško to Baško-Melnbārde. In February 2018 the couple divorced.