(1) Privilege doesn't necessarily negate disadvantage/adversity. Growing up in a rural area is certainly a disadvantage to medicine, so despite growing up with some privilege it has likely caused some difficulties. And depending on where your the school is, it likely adds diversity to the class (i.e. if you're writing for ETSU, probably doesn't add diversity...if you're writing for NYU, it probably does).
(2) It is absolutely okay to do a little bit of double dipping...especially if you writing about it in your personal statement was in the context of developing an interest in medicine, and not in the context of you facing adversity. It's okay to mention bullying, although adcoms do love a story of overcoming too so be sure to mention how you overcame it. This will demonstrate adversity and add diversity to your class. Good luck!
Edit: Wrt body building/sports, yeah probably wouldn't mention those in the context of diversity/adversity unless you faced unique barriers, or participated competitively at the collegiate level and/or won awards post-HS.