Naive
Bertie is not as naive as he likes to make people believe. They think he doesn't know how some talk about him. Well, he thinks to himself, just let them talk, as long as it stays talk only. Of course it's tiring to keep playing the oblivious clown time and time again - the one you can't take seriously - the fool who knows nothing of the real world. Thought to be immature, helpless in every aspect. All the more astounding they talk about his… hm, his personal gentleman as well. Malicious tongues claim there is something not quite right with him, something amiss, something queer. Bertie's and Jeeves' long-lasting friendship is looked upon with suspicious eyes, one could even say kept a very close watch on - too long it seems have the two been living alone together (quite happily, at that), when neither of them have ever been wanting of eager women… - that Jeeves is Bertie's valet becomes of little importance in the eye of such odd behaviour.
If Bertie weren't so naive, so oblivious, Jeeves not so cold (politely so, but cold nonetheless), so obstinate - one could easily get the wrong idea.
Bertie would associate a lot of words with his gentleman; cold isn't one of them.