I was watching ANH last night and Leia's lines when she first seens Vader ("vader, only you could be so bold") and Tarkin ("foul stench when I was bought aboard") made me think: she obviously had met both before, in the imperial senate, or in other political situations. Maybe Vader WAS in Alderaan once, and talked to her about her "merciful missions" and whatever.

My point is: what about Bail Organa? Wasn't him at least a liiiiittle bit scared to have Leia and Vader together in the same room? I mean, he knows Vader is Anakin, right? At any moment Vader could feel something and say "Waaait a second... Bail Organa, you feelings betray you! Leia is my daughter!". Am I right?