Jane is a character who we never actually meet in the novel. Her importance lies in the way that she is obviously one of the few women in the novel that Holden both likes and has a friendship with, and finds attractive. What is interesting about Holden's relationship with Jane is that he clearly feels protective towards her, and this could mask his own attraction that he is perhaps unaware of. Note what he says after Stradlater leaves for his date with her:
I sat there for a half hour after he left. I mean I just sat in my chair, not doing anything. I kept thinking about Jane, and about Stradlater having a date with her and all. It made me so nervous I nearly went crazy. I already told you what a sexy bastard Stradlater was.
Jane then is another example of how un-self-aware Holden is as a character, as he seems blind to his own feelings towards her.
Holden does not reach out to Jane and go down and see her, because he says he is not in the "mood" right at that stage. Perhaps he feels embarrassed or ashamed because he has just been kicked out of his school. He certainly asks Stradlater not to tell her about it. Whatever his reasons, it is interesting to reflect that Jane might have been one of the few people that Holden could actually have told about some of the deep unresolved issues that were going on inside of him. He refuses however to cry out for help until he has a breakdown.