Among other major influences on her work, she lists cellists Anner Bylsma, Jacqueline du Pré and Bruno Guiranna.
He also made a second recording of the same music in 1992 on the large Servais Stradivarius and on a five-string violoncello piccolo.
Bijlsma is the daughter of cellist Anner Bijlsma and violinist Vera Beths and the sister of actress Katja Herbers.
Having studied with Antonio Janigro, Antonio Meneses, Anner Bylsma and Hidemi Suzuki, he developed special interest in early music interpretation on period instruments.
He also appeared with such musicians as Anner Bylsma, Nancy Argenta, Simon Standage, Ronald Brautigam, Wieland Kuijken, Alexei Lubimov and many others and on such American festivals as Ravinia and Santa Fe Chamber Music Festivals and German ones such as Schleswig-Holstein Musik and Berliner Festspiele.
In recent years Kullberg has been specializing in the solo cello suites by J. S. Bach under the guidance of Dutch baroque cellist Anner Bylsma.
He was personally invited by Anner Bijlsma to perform in a Dutch documentary film on Luigi Boccherini and Anner Bijlsma, filmed in Arenas de San Pedro, Spain, where the composer lived the last years of his life.