All the references he makes in the books, or most of them are from the 1930s. From about 1933-1939. The thing with Bertie is that he never really seems to age, but if we take him to be 24 when Jeeves entered his employment, and that was in the early 30s, he'd have been in his late thirties by the time WWII broke out.

I do support the idea, actually, that Jeeves would have been cautious and up to date enough on currrent affairs to get Bertie out of the line of fire and move him to America (or possibly even Australia) well in time before anything truly serious could ever happen. And in doing so he'd have kept Bertie blissfully clueless and innocent. I think corruption is the worst thing one could ever do to Bertram W. Or the cruelest anyway.