Bail Organa mentioned how his wife had always wanted to adopt a baby girl. It was also imperative that the Skywalker twins were to be kept as far away from the Sith as possible, with their existence and identities kept secret. Given how the Sith operate, it would be prudent to have as few people know the truth as possible.
Therefore, there was good reason for Bail Organa to just bring Leia to his wife and go "Hey honey look, I just adopted a baby girl just like you always wanted!" without ever mentioning how she's the daughter of Anakin Skywalker and Padme Amidala - highly scandalous and controversial news considering recent events.
But did he? Did Bail Organa tell his wife nothing about Leia's parentage?