He studied double bass at the Kroměříž Conservatory with Alois Kríž (1963-68), and continued his studies at the Brno JAMU with Jiří Bortlíček, where he also studied composition with Zdeňko Zouhar (1968-72). In 1976, 1977 and 1979 he studied double bass with Ludwig Streicher at summer courses in Weimar. He is the laureate of the Tchaikovsky competition in Moscow and the winner of the jury prize in Munich, in 1976 and 1977 he was awarded at the international double bass competition in Markneukirchen.

During his studies, he played the double bass in the orchestra of the Janáček Theater in Brno (1968–69) and the Working Gottwald Philharmonic (now Zlín, 1969–73). As a concert artist, he performed at solo recitals (among others at the ISB conferences in Mittenwald 1991 and Houston 1997) and accompanied by an orchestra (1987 Czechoslovak premiere of Bottesini’s concerto in F minor with the Moravian Philharmonic Olomouc). In 1995, he made the first of five concert trips to the USA, playing in Boulder and Chicago. In 1978, F. Gregory founded the Bass club and the international double bass competition in Kromezíž. In 2000, he became a co-founder of the international company J.M. Sperger Michaelstein.
His pedagogical activity is significant. Since 1971, he has been teaching at the Pavel Jozef Vejvanovský Conservatory in Kroměříž, he also briefly worked at the University of Ostrava (1993-95). He is a lecturer at seminars and courses here and abroad: Brno, Bratislava, Moscow, Lodz, Debrecen, Subotica, Miskolc, Munich, Dresden, Berlin, Wells, Wroclaw, Denton, Madison and elsewhere. He gave master classes in 1997 at the Juilliard School of Music in New York. His pupils include, among others, Radomír Žalud, Miloslav Bubeníček, Roman Koudelka, Radoslav Šašina, Miloslav Jelínek, Pavol Klečka, Martin Šranko, Eva Šašinková, Luděk Zakopal, Miloslav Raisigl, Petr Ries and Jan Staněk. He is a regular member of the juries of conservatory competitions and many international competitions.
He is also active as a composer, in addition to chamber and spiritual compositions, he composes primarily for his instrument, in the cast of double bass solo (Sen konrtrabasisty 1976, Semper flageoletti 1998) to five (Chanson triste, Scherzino) and even sixteen double basses (Sexde).
In addition to the double bass, Gajdoš devoted himself to choirmaster work – he was the choirmaster of the Temple Male Choir in Zlín (1970-71) and the Moravian Mixed Choir in Kroměříž (1975-76), in the years 1971-89 he regularly collaborated with the Temple Choir. He was also the conductor of the Kroměříž Chamber Orchestra Capella Baroca (1974-92) and occasionally the organist and regenschoir of the church Bl. P. Márie in Kroměříž.