Bavelas represented his native country in the doubles competition at the 1988 Summer Olympics in Seoul, partnering George Kalovelonis. The pair was eliminated in the first round there. He also competed at the 1992 Summer Olympics.
The left-hander Bavelas represented Greece in the Davis Cup from 1984–1994, posting a 15-13 record in singles and a 5-3 record in doubles.
Bevalas played in some dozen minor circuit events during the 1980s. He highest ranking in singles was World No. 451, which he reached in November, 1984. His highest doubles ranking was World No. 438, which he reached in July, 1986.
Bavelas has been praised as the greatest natural tennis talent Greece has produced.