2000-2004 graduated from Vilnius University in Comparative Asian Studies with a Bachelor's degree in Sinology . 2004-2005 Studied Chinese language and culture at Taipei University (Taiwan). In 2006, she graduated from the UNESCO Department of Vilnius Academy of Arts with a Master's degree in Cultural Management and Cultural Policy.

During her studies, Biliūnaitė worked as a curator of exhibitions and symposia, assistant director at a video production company, editor of the page dedicated to the East in the cultural weekly "Šiaurės Atėnai", and coordinator of the international programmes of Lithuanian Writers' Union. In 2006-2007, she curated the foreign programme of Poetry Spring, the experimental audiovisual poetry festival Sintezija, and was one of the initiators and administrators of the literary culture platform www.rasytojai.lt.

In 2007-2013, she worked as a producer and event organiser at the Lithuanian National Opera and Ballet Theatre. From 2013 to 2015, she was the Head of the Creators Group of the Creative Partnerships Project of the Lithuanian Ministry of Education and Science's Development Centre for Creative Learning.

Appointed in September 2015, from 2015 to 2019 Biliūnaitė was the Cultural Attaché at the Embassy of the Republic of Lithuania in the People's Republic of China, the first Lithuanian diplomat to hold such a post in China.

Since June 2019, A. Biliūnaitė has been the Editor-in-Chief of LRT's cultural volume, responsible for the policy of broadcasting cultural news, curating cultural topics and their integration across all channels of the public broadcaster.

Since 2011, A. Biliūnaitė has been the editor-in-chief of the web portal www.mediascena.lt, a creator and collaborator of the web portal www.kafehauzas.lt, writing texts on theatre, opera, dance, new circus, and since 2012, a creator and collaborator of the web portal www.kafehauzas.lt (together with her brother, Kostas Biliūnas) and, since 2014, the Director of the public institution Kultūros virtuvė.