Bryndís Pálsdóttir completed her soloist diploma from the Reykjavík College of Music in the spring of 1984, after studying with Björn Ólafsson, Guðný Guðmundsdóttir, and Mark Reedman. She then continued her violin studies at the Juilliard School in New York, where she studied with Dorothy Delay, Hyo Kang, and Zinaida Gilels, completing her bachelor's degree in the spring of 1987 and a master's degree in 1988. The following year, she studied with Prof. Herman Krebbers in Amsterdam.

Since 1989, she has been a member of the Iceland Symphony Orchestra in addition to teaching at the Reykjavík College of Music. She has performed as a soloist with the Iceland Symphony Orchestra, given solo recitals, and performed various types of chamber music both in Iceland and abroad. She is a member of the Camerarctica string quartet, which has, among other works, performed the string quartets of Bartók and Shostakovich at the Chamber Music Society’ s concerts. With the oboe quartet Dísur, she has premiered many works by Icelandic composers and performed most of the major works written for this instrumental arrangement. She has also performed with the Reykjavík Chamber Orchestra, the music group Caput, in various National Theatre productions, in the Icelandic Opera orchestra, and the North Iceland Symphony Orchestra.