His visit comes just after the Progress Party, the junior partner in the country's coalition government voted to try to prevent the the country hosting the games, arguing that it would divert funds from necessary infrastructure.
According to a recent poll, as many as 60 percent of Norwegians are against Norway's hosting the Olympics in 2022.
During his visit, Bach argued that the fear that the costs of Olympic Games inevitably spiral out of control, was not borne out by the facts.
"People are sitting with a false impression that the Olympics is costing more and more, especially in connection with Sochi, and it is wrong," Bach told reporters. "Sochi cost no more than Vancouver, and the event was actually in surplus at the end."
He stressed that Sochi was also a special case, as most of the infrastructure had to be built especially for the event.
"If the required infrastructure is already in place, then it will be cheaper than if you create a new city, as happened in Sochi," he said.
Bach's visit, to visit the facilities for the 2016 Youth Olympics, had been arranged before the Progress party vote at the start of this month.
As well as meeting the secretary general of Norway's Olympic Committee, Inge Andersen, Bach had an audience with Norway's King Harald.
Oslo is vying with Krakow in Poland, Almaty in Kazakhstan, Lviv in Ukraine and Beijing in China.
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At a news conference, Bach denied favouring the Oslo bid.
"We cannot enter into the discussions into the bid or give advice to a bid," he said. "We will respect this procedure. And we are happy that all our partners respect this as well."