Inmates with high public profiles receive more attention than most people realize. Letters, emails, and pen pal requests come in regularly for anyone whose name carries recognition, and standing out in that crowd takes more than enthusiasm.
The most straightforward approach is a well-written letter that says something real. Not flattery, not obsession, just a genuine introduction that gives her a reason to write back. Inmates have time to read, and a letter that is honest, interesting, and respectful is far more likely to get a response than one that leads with how famous she is or how long you have followed her.
Right now she has something she did not have on the outside: time. The daily noise of a public life is gone. Many high-profile inmates find that correspondence with people they would never have connected with otherwise becomes genuinely meaningful during a sentence. That is the window you are working with.
Keep it simple. Be yourself. Send the letter through InmateAid if you want your personal address kept private, which is worth considering when reaching out to someone with a public profile. Then let her respond if she chooses to.
You will not have a better opportunity than right now.