Shteinbuk was born in Babruysk, Belarus. Her mother was a teacher, and her father, Gennady Shteinbuk, was a football and hockey coach in Belarus for the clubs FC Belshina Bobruisk and Shinnik Bobruisk. At the age of five, Shteinbuk began her piano studies. Later on, she left her hometown and moved to Minsk to continue studying music at school and at the Conservatory of Minsk. Shteinbuk has an advanced title from the Music Academy of Minsk (Belarus). In 1994, she moved to Israel with her husband and son. During her early years in Israel, she focused mainly on teaching piano and rarely performed for large audiences. After a year in Herzliya, where she taught piano at the conservatory, the family moved to Rishon Lezion. Shteinbuk separated from her first husband and currently resides in Rishon Lezion. In August 2010, she married clarinetist Vladimir Chernomordik.
In 1991 Shteinbuk joined the "Classic Avantgarde" soloist ensemble in Minsk. She performed with the ensemble until 1994.
During this time, she appeared in several major music festivals worldwide:
- 1989, performed at the International Festival in Vitebsk named Sulrtinsky (Sollertinsky).
- 1991, Helsinki, Finland – Festival of Modern Music
- 1992, Gelsenkirchen, Germany – III Gaida Forum- Festival of New Music
- 1992, Lvov, Ukraine – III International Music Art Festival Virtuosos
- 1992, Padova, Italy – Bienale
- 1992, Venice, Italy – Bienale
Later in the decade she made appearances at various locations throughout Europe:
- 1992–1994, Minsk, Belarus – Ancient Belarusian Music Festival "Revival of the Belarusian Capella"
- 1993, Bonn, Germany – Bonner Summer–93 International Music Festival
- 1993, Kaliningrad, Russia – XIII International Arts Festival Amber Necklace
- 1993, Kishinjev, Moldova – New Music Festival
- 1993, Kudowa-Zdrój, Poland – XXXII Festiwal Moniuszkowski
- 1993, Minsk(Belarus)- Warsaw-Gdansk (Poland) – Polish-Belarusian Musical Meetings Minsk-Warsaw-Gdansk
- 1993, Vilnius, Lithuania – III Baltic Music Festival
- 1994, Berlin, Germany – Kreuzberger Hofkonzerte Im Podewil
- In 1995, Shteinbuk performed at the International Tchaikovsky Competition for Young Musicians Sendai,Japan
From 1995 Shteinbuk taught music at the Conservatory of Kfar Saba, Israel
At the turn of the millennium, she created a number of albums, including two international albums recorded in Canada. During the decade, she appeared in many international festivals, including festivals in Mexico, Canada, the United States and Spain.
During 2004–2005, she took part in the "Three Tenors" (Gabi Sadeh,Yotam Cohen and Felix Livshitz) show in the U.S., as well as the finals "Film Festival" in Toronto, Canada (European Union Film Festival).
From 2004, she played in the Israeli ensemble Bellamiya.
26 May 2008 appeared at the festival 10 San Miguel de Allende, Mexico.
2010 – performs three concerts in New York City.
On October 17, 2012 she appeared at the XXXVІII International Festival of Arts "Belarusian Musical Autumn": International Music Forum "Belarusians of the world" with ensemble of soloists "Classic-Avangarde" in Minsk, Belarus.
Between November 13–15, 2012 Bella provided several Master Classes in Belarus, including some at the Belarusian State Academy of Music in Minsk, Minsk State Music College name MI Glinka and more.
On November 15, 2012 she appeared as part of a festive concert celebrating 20 years of friendship between Russia and Israel, held in Minsk, the capital of Belarus. The concert was covered extensively in the media of the Jewish community in Belarus. In 2011, Shteinbuk was nominated for the title of "Man of the Year" in Rishon Letzion in music and art of the former Soviet Union. By the year 2014 she made appearances at festivals and concert halls in Israel, including the Mann Auditorium in Tel Aviv, Tsavta TA, Abu Gosh Festival, in the "Marathon operatic" International Music Festival in Eilat and more. As of early 2014, Shteinbuk teaches music at the Conservatory of Kfar Saba and holds a career of concerts and various shows.