She was probably being ironic. Elayne would almost certainly have mentioned her title at some point or other, with Birgitte maybe being skeptical, and definitely disbelieving after so long with her in the menagerie.

Circus performers have always had a low social position and in some older times and cultures in the real world, performers were merely one short step above prostitutes. That may be one reason why Shakespear infamously only had male actors (and hence, very few instances of kissing, despite all the dirty jokes and obscene puns) - decent women just did not do that sort of thing, and other decent people would not publically attend a display of indecent women.
While that is almost certainly not the extreme case in the world of WoT, that very same menagerie, only grown much larger and more presitigious is still rather low on the totem pole as we see in KoD. Elayne & Nynaeve had very good reasons for believing Galad would never look for them among the circus folk - a strange assertion regarding someone who knows the two of them and exactly how impetuous and undauntable they could be. On the other hand, another trait they share besides audacity in action is modesty and propriety, moreso than any other of the main female characters. For someone who knows them as well as Galad, the idea of them hiding among the circus folk is almost as absurd as in a brothel.
With that in mind, Birgitte's observation of Elayne as a performer, not to mention her costume and the rather immature depths to which she and Nynaeve sank in their relationship during this period, it is not hard to see where Birgitte comes by her skepticism of Elayne's claim to be the heir to the throne of one of the most powerful and respectable nations in the known world (Andoran women seem to have the most modest clothing and traditional female roles).