I want to make clear that teaching, or educating, a child that something is bad / rude, is different from making the child stop that bad behaviour. And your question is specifically about how to educate the child:
how to make her understand eavesdropping is rude without getting the impression that you, or other dear people, hide things from her and each other.
I repeated your question, with some minor changes, in order to be sure I understand it.
First thing that comes up to my mind is why not? Let her get that impression. Is it bad? You said you've got nothing to hide from her. On the other hand you also said that you're careful not to be "interesting" unless she's sound asleep. So there are things for which we wish neither her intervention nor her knowing. What's wrong with that? it's totally legitimate to have secrets. We all have secrets and it's fine. Secrets aren't necessarily bad ones, they are not necessarily against the others or against someone at all. On the contrary. There are matters that are better not be shared with children of too early an age, things that they still cannot digest, things that might harm them. So it's not only legitimate, it's a necessity.
In fact, with time, there will probably be some "secrets" that are shared between you and your child and you'd ask her to hide it from someone, say a neighbour. Since you aim to be a well-behaving person (according to whatever morals you follow), you'd have a good / legitimate reason for hiding it. That's actually great, since this way your child will learn how to use the power of secrets for the right purposes. It's the natural way children, and we all, learn (guess you know that).
What I would fear of, is that she might be insulted. She'll understand you want her not to listen, but she won't understand why. And then she might interpret it as "my parents don't love me" and the such (not ultimately don't love, just this-very-moment-don't-love).
So my suggestion is to be natural about it. If you want privacy that your child doesn't yet naturally give - explicitly and kindly ask for it. Try to avoid this situation, though, as much as possible, in order not to insult her. She'll mature, regarding this aspect, and grow to understand this important social skill.