Ease Me In (The more guarded approach):
Before I ask you my next question, I just wanted to make 100% sure that everything between us is private. I trust your advice, so I wanted to talk about birth control and hopefully get a method today, but I don't want anyone else to find out.
Just Give It to Me (The no-nonsense tactic):
I know that we have the whole doctor-patient confidentiality thing, but I want to talk to you about birth control and am a little uneasy doing it because you know [family member/friend]. This all stays totally between us, right?