As a father, and (almost) a Mason.. Allow me to give you a different perspective not yet voiced..
Each daughter has their own unique relationship to their father. I have instilled my daughter with the impression, since she was 10, that any boyfriend she may have, will need to go through me.
When she turned 18, I informed her that so long as she is living in my house (she still lives at home to her mothers, and my, delight) it is required that I meet anyone she goes out with before hand.
Some people may think this is way overboard and unneeded. To that I would respond with this comment.. “I was a young man myself at one point and I will leave it at that.”
So far, I have met every single friend she has and have not had any concerns with them. I am happy to say, that I have only questioned 1 outfit she was going out in (once in her life time).
I truly believe that my daughter would respect my wishes in this area, as it would only be to help protect her.
So, in short, when you ask HER to start dating, offer to meet her parents (you have stated that you do not know them well) if she wishes. To me, this shows genuine intent.