Sheida began learning the cello at the age of four with Wendy Max and her teachers have included Joan Dickson, Florence Hooton, David Strange and Stefan Popov. In July 2000 she graduated with first-class Honours from the Guildhall School of Music and Drama and was awarded the Peter Latham Leaving Scholarship. She has since completed a year of study at the Hochschule für Musik in Cologne with Maria Kliegel and a Master of Music degree and Orchestral Studies Diploma (with the Rochester Philharmonic Orchestra) at the Eastman School of Music in the USA with Steven Doane and Rosemary Elliott. Her studies were supported generously by the Countess of Munster Musical Trust, the Eastman School of Music and the P.E.O. Sisterhood International Peace Scholarship Fund.

Sheida has taken part in international masterclasses in England, France, Germany, Switzerland, Italy and Bulgaria with professors such as Robert Cohen, Gary Hoffman and Gerhard Mantel. The most noteworthy were the Manchester International Cello Festival and the Festi-Val Gardena in Italy, where she also had the opportunity to perform chamber works with the late Norbert Brainin, violinist of the Amadeus Quartet.

As a chamber musician Sheida attended the International Musicians Seminar in Prussia Cove, Cornwall (Sigmund Nissel) and the Sándor Végh International Chamber Music Academy in Prague. She has performed in the BBC Martinu Festival, the Spitalfields Festival, the Conway Hall and Linbury Studio Theatre as part of the Park Lane Group Concerts. She has appeared at the Wigmore Hall, the Symphony Hall Birmingham and on BBC television as part of a lecture series on Beethoven by John Suchet. She also plays regularly for the charity Music in Hospitals.

Sheida was appointed principal cello of the National Youth Orchestra of Great Britain in 1996 and was a member of the European Union Youth Orchestra from 1998-99. From 2001-2004 she participated in the Countess of Munster Musical Trust Recital Scheme appearing at many prestigious venues and festivals around the UK. Recent performances include the Elgar Concerto with the Thames Philharmonia and recitals with pianist Helen Reid at St. James's Piccadilly, Farnham Castle for the Tilford Bach Society, the National Portrait Gallery, St. John's Smith Square and BBC Radio 3's 'In Tune' to celebrate the centenary of British composers Constant Lambert and Alan Rawsthorne. As a chamber musician she performed at Hatchlands Park with the London Pleyel Trio to celebrate bicentenary of Frederick Chopin.

Sheida has plays on a cello made by Thomas Kennedy.