Bail and his wife raised her from birth as their own, because they couldn't have children, this could explain her adopted 'mother's sadness at not being able to conceive a child of her own, concealing Leia's identity from her true father and the Emperor, whilst still retaining a position in the Senate would be hard enough without letting Leia know she was adopted, as far as I know Leia was unaware that Bail Organa was not her natural father.
Bail and his wife raised her from birth as their own, because they couldn't have children, this could explain her adopted 'mother's sadness at not being able to conceive a child of her own, concealing Leia's identity from her true father and the Emperor, whilst still retaining a position in the Senate would be hard enough without letting Leia know she was adopted, as far as I know Leia was unaware that Bail Organa was not her natural father.