Much to my surprise, I've had that kind of sentence copy-edited to no question mark, I assume because the whole sentence isn't a question even though some of it is.
It's the same principle as:
What on earth should I be doing now, I wondered.
which doesn't have one either. Yes, I think it's odd too, but the alternatives - in your example after 'now' or 'ask' - are odder, I guess.
I would either leave out the question mark or put it after 'ask', because there could be an intonation rise there. It depends how much you want 'I hear you ask?' to sound like a question.
I think 'I wondered' is different because it's definitely declarative. 'I hear you ask' could be declarative or interrogative depending on the effect you're going for. In my humble opinion...
I always believed you should (in Nikki's example) put the question mark at the end of the whole sentence, because part of it is a question. But perhaps that's wrong?
I'm not sure it's correct, but it makes a lot of sense. One of my options (again, not sure if it's correct, but it's very clear) is to use italics for any speech that's remembered or imagined:
And why would I want to do that? I hear you ask.
Emma
<Added>
And Luisa, I'm interested that you're partly going on the inflection, rather than the grammar. When my punctuation gets picked up by a copy editor it's nearly always because I've punctuated for how it would read, rather than what's correct. Maybe it's partly because - like Nikki's example - I'm almost always writing in someone's voice, and hearing it as I write.
Good point, Emma, and I've course I'm biasing this towards the way I write, which is always very strongly in someone's voice. (Like Nikki too, I'm pretty sure.) I'm going to get copy-edited to bits soon.
Of course, Nikki asked for 'the correct way', not for my descriptive opinion. Sorry, Nikki!