Pistorius and Steenkamp met Nov. 4 at the Kyalami race track, which sits between Pretoria and Johannesburg and has been used for Grand Prix and Formula 1 races, said Justin Divaris, a mutual friend.
Divaris said his own girlfriend was a close friend to Steenkamp. Pistorius and Steenkamp immediately hit it off and decided in the spur of the moment to attend a sports award ceremony together the same night, Divaris said. At the time, Pistorius had been dating another woman and his personal life was constant fodder for gossip pages.
Later, however, problems may have started, as police have said there were previous domestic altercations at Pretorius' home in a gated community near South Africa's capital, Pretoria.
A Steenkamp family spokesman said late Friday that relatives still faced a long struggle to come to terms with her killing.
"I can't see the family getting over this shortly," said Reeva's uncle, Mike Steenkamp. "It's going to be a long, long-term reconciliation with a lot of things and issues."
Family members plan for a memorial service Tuesday for the model in Port Elizabeth, her hometown on South Africa's southern coast. Pistorius has a court appearance scheduled in Pretoria on the same day for his lawyers to argue that he can be released on bail.
Portions released earlier Saturday of the reality show, sponsored by a milk fruit drink, feature Steenkamp laughing and smiling on the beaches of Jamaica. Another portion shows her swimming with two dolphins, which tap her on the cheek with their snouts.
"I think the way that you go out, not just your journey in life, but the way that you go out and the way you make your exit is so important," Steenkamp says in the video. "You either made an impact in a positive or a negative way, but just maintain integrity and maintain class and just remain true to yourself.
"I'm going to miss you all so much and I love you very, very much."
Associated Press writer Jon Gambrell contributed to this report.
Gerald Imray can be reached at http://twitter.com/GeraldImrayAP