By the time of his international debut for Canada, at the 1966 British Empire and Commonwealth Games, Bob Kasting had set numerous national swimming records. At the Games Kasting took silver in the 4x110 and 4x220 yard freestyle relays, with Ralph Hutton, Ron Jacks, and Sandy Gilchrist in both. His next stop was the 1967 Pan American Games, where he earned another silver medal in the 4x100 metre freestyle relay, again with Gilchrist, Hutton, and Jacks. He was an alternate for the relay teams at the 1968 Summer Olympics, but did not compete. At the 1970 Commonwealth Games, however, he took home medals in all of the relays: gold in the 4x100 m medley (alongside Bill Kennedy, Byron MacDonald, and Bill Mahony) and silver in the 4x100 and 4x200 m freestyle (both with Hutton, Jacks, and George Smith). He then captured silver in the 4x100 and 4x200 m freestyle relays at the 1971 Pan American Games (alongside Timothy Bach, Ian MacKenzie, and Brian Phillips in the former, and Hutton, Jacks, and Phillips in the latter), as well as bronze in the 100 m freestyle. He was then selected as the captain of the swim team at the 1972 Summer Olympics, where he won bronze in the 4x100 m medley relay with Kennedy, Mahony, Erik Fish, and Bruce Robertson. He was also fifth in the 4x100 m freestyle relay, alongside Bach, Phillips, and Robertson, and eliminated in the semifinals of the 100 m freestyle and butterfly events.
Kasting graduated from Yale University in his Olympic year, having captained the swim team as a senior. He continued to swim for several years after the Games, even as he earned a diploma from the University of Stockholm and entered McGill University to study law, but he failed to qualify for the 1976 Olympic team. He retired from active competition shortly thereafter and was called to the British Columbia bar in 1978. Since then he has practiced law in Vancouver and, in 1997, he was made a member of the Lethbridge Sports Hall of Fame.