After the failure of the Hungarian Revolution of 1956, Berger left Hungary for Australia, where he won the New South Wales state title in 1957 and 1961. He played in the Australian Championship in Sydney in 1958/59, finishing second with 11.5 points, behind Lajos Steiner's 12.5.
National champion John Purdy was one of Australia's two representatives at the 1963 Pacific Zone 10 Championship in Jakarta. There was a quadrangular selection tournament in Melbourne for the second spot. Bela Berger and Karlis Ozols tied for first; the selectors voted in favour of Berger 3-0.
In Jakarta, he tied for first with Indonesia's Arovah Bachtiar on 5.5/8, and won the playoff 2-1 after 3 games. A fourth game was won by Bachtiar, but it had no bearing on the outcome, as the tiebreak system used favoured Berger. As zonal champion, he became an International Master.
He went on to play in the 1964 Interzonal tournament in Amsterdam, with 18 grandmasters and 6 international masters, finishing 23rd out of 24. The joint winners were Vassily Smyslov, Bent Larsen, Mikhail Tal and Boris Spassky. Berger tied for 7-8th at Manila 1968 (Meralco Open, Svetozar Gligorić won).
In 1991, he won a short match against Charles Pizzato (2 : 0).