At age six Špitková started her studies at her local music school. She studied at Bratislava Conservatory under Albín Vrtel. During this period she performed as a CSSR cultural ambassador, along with fellow ambassadors Edita Gruberová and Marián Lapšanský, in Germany, Great Britain, Italy, Poland, the Netherlands and Switzerland. After five years of study, Špitková toured Great Britain with the Slovak Philharmonic and the Brahms Violin Ensemble. One year later she became concertmaster of the European Union Youth Orchestra under Yehudi Menuhin.
On 19 April 1968 Špitková performed the Tchaikovsky violin concerto at the concert hall of the Slovak Philharmonic. She finished her studies in Bratislava as “the best graduate of the year”. In the summer of 1968 she won prizes at international competitions in Sofia and Sion. In 1968 Špitková stayed in Vienna, where she met Ricardo Odnoposoff. He admitted her to his violin class at the Vienna Music University. She finished her studies under Odnoposoff in 1970 and contracted with the "Slovkoncert" concert agency. Besides her studies in Vienna and her concerts, Špitková studied in Prague at the music academy and finished her studies again as “best graduate of the year”. She studied under Alexander Plocek. Her graduation concert was with the Symphony Orchestra of Prague and the Brahms violin ensemble. Because of problems with her visa, Špitková could not become a member of the English Chamber Orchestra.
After her studies, Špitková was appointed “soloist of the Slovak Philharmonic”. She founded the Suchoň Quartet and the Slovakian Trio, gave televised concerts, and made many recordings. She performed with the Bratislava Women's Chamber Orchestra. From 1975 until 1980 Špitková gave more than 800 concerts in 60 countries. In 1979 she was appointed concertmaster of the Radio symphony orchestra of Copenhagen. Špitková then became concertmaster of the Mozarteum Orchestra and was also concertmaster of the Gärtnerplatz - Theater Orchestra in Munich. She produced many recordings and also performed as a soloist. Špitková was concertmaster of the Vienna Bach Soloists and the Orchestra Sinfonica Brasileira.
Špitková was awarded prizes at the Marguerite Long-Jacques Thibault competition in Paris, the J.S.Bach violin competition in Leipzig, The George Enescu competition in Bucharest, a competition for young musicians in Sofia, The Carl Flesch violin competition in London and the ARD - Violinwetbewerb in München.
Family life
Her mother was Olga Špitková, née Bogyayová, graduate of the Faculty of Economics in Bratislava. She worked at a bank. She concentrated on oil painting. Her father was Dr. Pavel Špitka, a lawyer. He played the organ and piano and was a church organist for about 40 years. Her brother was Igor Špitka, a violinist of the Slovak Philharmonic