I think he was 50 when this was filmed, but you're right - really kinda old for the part even if they're supposed to be mid 30s. The thing is that Der Bingle was much loved in post war America and that it was his version of the song White Christmas everyone knew. I suppose everyone back then ignored his age as I do now. I'm glad he played Bob Wallace. And really, Danny Kaye was no spring chicken at 42 either.
And if I uderstood what they said correctly, Bing originally turned the film down because he thought he was too old. Then the studio hired a writer at an exhorbitant sum to rewrite the script in such a way that would make Bing more comfortable with taking the role. The script was indeed rewritten and then Bing did indeed say yes. It makes me wonder what the original script was like.