I was intrigued by what Tim Minear had to say about Inara's secret during his commentary on "Out of Gas" with director David Solomon. Tim first mentions it during the scene when Simon and Inara are sitting in the lounge outside of the med bay, talking about possible suffocation.
Commentary during that scene:
Tim: There's a whole Inara story that we didn't get to tell, that you'll see in episodes little clues, and there is a clue in this scene, in the dialogue, which I will not give away.
David: Give it away, I don't know it!
Tim: I'm not gonna give it away --
David: (interrupting) Okay.
Tim: -- 'cause it may show up in some other form.
David: Oh. (with realization) Ohhhh.
Later on, when Inara and Mal first meet and talk in what will become her shuttle, Tim mentions there's another clue in this scene.
Tim: And a few more of those little clues are dropped into this scene, by the way.
David: Oh, about what's gonna happen with her?
Tim: Yeah, I mean, this notion he's wondering why somebody like her who could get on basically, the Love Boat or um, you know, some giant Carnival cruise ship of the future, wants to fly on this tin can.
Tim: She's clearly got a secret. She's clearly, if not running from something, running to something.
David: Well, he asks her as much, though.
Tim: Yeah, and she denies it.
I've been trying to figure out what the potential clues could be, and I keep arriving at the conclusion that Inara needs to be on Serenity for some reason other than her companion duties. I think she is running to Serenity, although I haven't figured out what the "secret" is compelling her to do so. In the second scene, she tries to make Mal feel like he needs her presence on board to be respectable, but I'm reading that Inara desperately wants to be on that ship, and she's just trying to turn the situation around and make him think he needs her on board, not the other way around.
I'm probably fishing too much at this point, but looking at this dialogue in the lounge --
Inara: I love this ship. I have from the first moment I saw it.
Simon: I just don't want to die on it.
Inara: I don't want to die at all.
-- I wonder about two possible interpretations. One, could Inara have come across Serenity earlier than when she first talked to Mal, and does that play into her reasons for wanting to be aboard? Two, (and this is waaaaay out there) thinking back to Darla and syphillis on Angel, is there something about Inara's health we don't know? Because of the companion standards, that doesn't seem very plausible, but it crossed my mind when examining the dialogue for clues. Also, if you read (way too) deeply into her nonverbal reaction to Simon saying it was his birthday, assuming there's something about her past drawing her to the ship, does a birthday have to do with it?
This is all wild speculation on my part, but it's an interesting parallel to the more obvious questions raised about Book's history.