Haven't really come across private profiles before.
does it show any of the bullet point interests?
but id say do it like any other....
unique catchy sarcastic subject.... then first line in the body to close the subject off.
then call her on it..
"why hello there "private profile" i figured you'd like a change from your normal lurking about in the shadows creeping others profiles and have someone say something to you. There is nothing on your profile to go on, but you do look kinda friendly and cute. Kinda mischievous though... are you a REAL trouble maker or you just have that look about you?"
or
subject... "blonde eh.... see at first i thought.....
body: ".....that you just didn't know how to work the computer.. cuz when I got to your profile there was NOTHING on it.. but then I noticed you're blonde and then immediately assumed ALL the thoughts you had in your head you just poured out in your profile.... leaving it how it looks now....

haha.... if you understand sarcasm maybe you'd be a cool person to meet. You look like a shopaholic and a hockey fan, am I right?"
she has a picture
shes on a dating site
doesnt leave you much...
you can comment about something in the picture...
or just call her on her private profile and what shes doing here...
she knows shes hot... she knows shes on a dating site.. so she knows shes gonna get msgs... stand out like with any regular profiled girl you msg.
private profile on a dating site though.. you might get a lot of read deleted or unread deleted.... she could be looking for chicks too and disguising it... who knows...
let us know how you make out..