What examples in A Separate Peace prove it as a bildungsroman or coming of age story?
"A Separate Peace" is a story about growing up and facing adulthood. The boys live and go to school in a very safe place at the Devon School, but as they mature, they learn from their mistakes and buckle under them as well. Because the book is written from Gene's adult perspective, he can interrupt at different points when telling the story to insert his reflections and what he learned at the time.
The boys at the school each have their different struggles to face. They are all under some disillusionment at some point when it comes to their future participation in the war. This disillusionment is exemplified by how each boy perceives the war. For example, Finny denies that there is a war after his leg is broken because he can't face the fact that he won't be able to participate in it. Once he does face the fact that there is a war, he also accepts himself and his disability. Gene, on the other hand, must face the fact that he hurt his best friend for life. Once he admits that to Finny, he grows up, but he also has to face it with others, too. Finny needed to face the fact that Gene hurt, him, too, in order mature and accept reality.
Leper is another boy in the story that must face his demons. He joins the war thinking that he would get to be on the ski patrol, but he wasn't ready mentally to accept the war and broke down before he could pass basic training. Shame, saddness and confusion force him to move backwards away from maturing and developing in a healthy way.
All of the themes in the novel deal with the boys facing adulthood; they face war, inner-self, the end of high school, and physical and mental limitations. No parents are around to pick them up; they must pick themselves up.
The link below seems to help answer some this a bit further.