From her mildly surprised expression (as opposed to her intense-shocked expression when a BO member or someone linked to the BO is near, lol), and the background which seems to indicate a somewhat serious and somewhat sad atmosphere, and also the fact that she never mentioned it to Conan afterwards, I'm guessing that it's something private, like:
"I'm really
sorry that you have to be involved in the Organisation as well, because of your father and me."
But if it actually translates to "The truth is, I..." then maybe it could be "The truth is, I'm really
glad that you chose to continue this research that your father and I have devoted our lives to."

but the 'maybe you're old enough to hear this' part potentially changes things.
I don't think Haibara would sit still if her mother had said "I'm really still alive...", she would probably try to contact her somehow even if her mother tells her not to.
Also I don't really buy the "I'm really Vermouth" theory because in the next few chapters Vermouth had a gun pointed at Haibara's head and in all probability would have shot if it hadn't been for Conan. :S