Bianca is in love with Varric; he is in love with her. Unfortunately, she had to marry someone she had no interest in for the benefit of her family. They're like Romeo and Juliet; the whole clan war thing, just without the weird murder-fest because of someone they'd know for like three days. Yet her own curiosity and misguided want to do good lead to Corypheus finding the Red Lyrium.
Yes, she feels guilty, perhaps more-so because Varric is disappointed in her rather than the fact that many people either died or got hurt because of her. (Unintentionally I stress.) - The last words to the Inquisitor, the perceived threat, is light-hearted enough to brush off because I feel, or at least MY Inquisitor feels that it is simply a woman who is afraid that the man she cares for might die following the Inquisitor into a situation she has no control over. She's worried, it doesn't mean that she would ever act upon it.
I'm sorry, are we talking about the same Bianca? The Bianca who left Varric at the altar to marry someone who she didn't love, and then continued an emotional affair with a man who lived half a world away because she didn't have the guts to tell him they should both move on? Yeah, Bianca is horrible, and I'm just not going to see it any other way unless they choose to clarify a few things for us.
I don't see their romance as being at all Romeo and Juliet (which was in of itself a bad romance). Bianca was arranged by her family to marry someone. She decided to marry Varric instead. Then, right when they were supposed to get married, she changed her mind again and married the other guy. She then kept Varric on an emotional leash while they lived hundreds of miles away from each other, hardly ever seeing or speaking to each other, and then she comes back and claims to be deeply invested in his life. Yeah, I'm gonna call BS on that one.
Not for one moment do I believe that she "had to" marry her now-husband. She could have run away, and if she's as amazing as they made her out to be, she could have done it with ease. If Zevran, who was chased by the most lethal guild of assassins in Antiva and possibly elsewhere, could not only escape from the Crows but then return, kill a bunch of their operatives, and a guild master, plus countless others, then Bianca could have easily run away with Varric. She just chose not to. And yes, I know some of you are going to say "she did it for her family!" But from what little we know of her, she was causing ruckus and chaos that was detrimental to her family and to the clans, and if she had left she might have been doing them a favor. And if she DID choose to stay to keep them from being hurt, then why did she let Varric stay attached to her rather than telling him that it wasn't going to work? As far as I can tell, she's got her cake and she's eating it too. She's got a wealthy, intelligent husband who seems to treat her well, and a hunky guy on the side to hook up with once every 10 years, if he's lucky. That's not love. That's stupid on his part and enormously selfish and egotistical on hers.
She feels guilty? GOOD. She SHOULD. Varric told her not to tell ANYONE about the thaig (which he shouldn't have told anyone about to begin with), told her to leave it alone, leave it buried, and what does she do? She lies and says she won't do it, then proceeds to do exactly what he told her not to, and guess what! Now we have FREAKING RED TEMPLARS! Do you want mass murder, Bianca? Because this is how we get mass murder!
As far as I'm concerned, Bianca has no right to demand anything of the Inquisitor or Varric. She gave up the right to ask for anything when she used secret information to satisfy her own curiosity, the result of which was nothing short of horrific.
In closing: We may not see much of Bianca, but what we do see of her tells me that she is not only a bad character, but also a misguided and selfish person. Meanwhile, Varric is a fool for staying tied to a woman who is married to another man (and who married him after she told Varric that she'd marry him), who he also sees once or twice a decade if he's lucky. This story's ending is going to be predictably tragic, and the truly tragic thing about it is that Varric will realize it as such only when the final page is written, before he has a chance to change anything.