This. She didn't know that Vader was her father yet (and George Lucas didn't either)
but bail organa was her "father" and kenobi served under the senate and bail organa was in the senate
Yes, I'm agreeing with you. When she said 'father' she doubtlessly meant Organa because she might not have even known she was adopted, and she definitely didn't know that Vader was her father, and George Lucas hadn't decided that yet either.
sorry, just misread it