He has established, and been a member of, many wind ensembles (the Corni di Bratislava, the Camerata Slovaca, the Bratislava Wind Octet, the Nova Brass, and the Bratislava Chamber Harmony). He often performs and records with the Cappella Istropolitana. He has also worked with the Ladies Chamber Orchestra, the Bratislava Chamber Soloists, and the Bratislava Wind Harmony; as a soloist, he has performed with the Salzburger Mozart-Serenaden and the Franz Lehár-Orchester in Vienna. He has recorded for Slovak Radio and Television. Budzák's solo repertoire comprises concert pieces ranging from the Baroque to those of 20th century composers, including Slovak compositions (both past and present). He has been involved with many modern works for the French horn, and has premiered a number of pieces by domestic and foreign composers.
He is a founding member of the Slovak Horn Society, of Hornfórum – the Czech Horn Society, and the International Horn Society in the USA.
He first taught at the Bratislava Conservatory, and since 1977, he has worked at the Academy of Performing Arts in Bratislava. His pupils are members of leading domestic ensembles, and many of them have permanent engagements abroad. He is a regular jurist at international performance competitions.
In 1999, he was the organiser and secretary of the first French horn performance competition in Slovakia, which took place in Bratislava. As a lecturer, he headed a seminar as part of the 5th Central European Festival of Concert Art in Žilina (1995), and in 2002, he ran a workshop at the 3rd Brass Seans international music festival in Bratislava.