At a very early age Anner Bylsma received the most significant part of his education from his father, who was a passionate musician himself. He studied at the Royal Conservatoire in the Hague - his native town - with Carel Boomkamp, a splendid teacher and musician, which resulted in a Prix d'Excellence. Bylsma was already principal cellist with the Netherlands Opera when in 1959 he won first prize at the Pablo Casals Competition in Mexico. From 1962 to 1968 he held the position of principal cellist of the Concertgebouw Orchestra in Amsterdam. During this time the early music movement was becoming more popular; this resulted in an increase of touring and recordings for Anner Bylsma with a number of well-known early music conductors including Frans Bruggen and Gustav Leonhard.

Anner Bylsma's career has included performances with chamber orchestras including the Freiburger Barock, Age of Enlightenment, Orpheus and Australian Chamber Orchestras and Tafelmusik. He has also given many recitals with fortepiano, pianoforte and harpsichord as well as concerts with his chamber group l 'Archibudelli.

Anner Bylsma's expertise as an early music cellist has kept him in demand as a recording artist. His recordings include works for the cello in the 17th century and by François Servais (Harmonia Mundi-BMG), many discs of works by Boccherini (BMG and Sony), as well as Dotzauer and Franchomme (Sony), and a number of performances on the rarely played cello piccolo. Mr Bylsma has also recorded extensively for Sony-Vivarte, both as a soloist and as a member of l'Archibudelli; among these are works by Mendelssohn, Mozart, Beethoven, Schubert and Bruckner, as well as Onslow, Michael Haydn, Gade, Spohr and Reicha. All these CDs have been extremely well received and have received many awards.

Anner Bylsma often takes time out of his busy performing schedule to give masterclasses at well-known institutions including the Paris Conservatory, the Berlin Hochschule and the Juilliard School in New York.