Ásdís returned to America to be a founding member of the Miami String Quartet, with whom she won the first prize of the Fischoff Chamber Music Competition and was professor of viola at the New World School of Arts. She became the principal viola of the Deutsche Kammerphilharmonie Bremen in 1990, where she worked closely with many great artists including Heinrich Shiff, Gidon Kremer, Walter Levine and Sandor Vegh.

In 1995 Ásdís joined the Chilingirian String Quartet and was their violist until 2003. She has been invited to many prestigious music festivals around the world, including Marlboro, Kuhmo, Lockenhaus, Davos, Berliner Festspiele, Prussia Cove, Bath, St. Nazaire and Prades, where she has performed and taught. She has appeared as soloist with the London Mozart Players, the London Soloists Chamber Orchestra, the Russian National Orchestra and the Iceland Symphony Orchestra and has been invited to work with many orchestras as guest principal viola. She now lives in Amsterdam, joined the Utrecht String Quartet from 2006 and teaches at the Utrecht Conservatory and at the International Masterclasses at Apeldoorn.