So I was wondering if I was the only one who caught this. In the beginning of the movie "X-Men Origins: Wolverine" we see Logan and Victor in all wars including World War II but in the movie "The Wolverine" he's trapped in a bunker in Hiroshima. How?
He was there in a bunker when the bomb goes off. However it doesn't imply that he was there during whole war. WW2 lasted for many years during which Wolverine fought in some battles and moved from place to place. Even after the bombing, he doesn't need to stay in the bunker more than a few days at most, due to his regenerative abilities.
According to wikia, he was there as war prisoner, which implies he indeed fought in some previous battles in WW2. Below is a text from wikia:
Sometime during 1945, James transfers from the European front to the Pacific front, where he is captured by Japanese forces prior to August 9, and is sent to a POW camp near Nagasaki. During the Nagasaki bombing on August 9, 1945, James saves the life of Ichirō Yashida, a young officer in the Japanese Imperial Army. After saving his life, Yashida thanks him and offers a Japanese samurai sword as a token gratitude. James refuses, but says to hold onto it for him, promising to return for it in the future.