Definitely give some thought to what you expect out of the interchange, and how it will affect you (and her) if it doesn't go the way you want. I think it's something you may want to sit on for a while.
Particularly remember that from her point of view, it can be a very disturbing experience, even if it can later end up in a good relationship. I don't know what her relationship with your dad is like, but she may be unprepared for you, the very physical manifestation of his lying to her (implicitly or explicitly).
I do agree that if you are ready to contact her, then a physical letter is a good way to go about it. It puts some time between you and her and without the immediacy of email gives her some space to figure out her response without pressure.
I would also try to give the sense in the letter that the ball is in her court. You don't want her to feel like you want to force a relationship on her, and you're prepared to never contact her again if that's what she wants. I think that would make her more open to talking with you.
This is basically what I've written:
Dear [Sis's name]-
I have written and re-written this letter both on paper and in my head hundreds of times. I'm not sure what, if anything, you know about me. In short, I am your sister. Technically, half-sister; Your dad is my biological father. I'm 33 years old and live in Ypsilanti. I grew up there and just recently moved back after spending ten years in Los Angeles, California. I am married and have a three year old daughter. She's the cutie in the picture. I'm the brunette.
I waited until you were an adult to contact you so that you could decide if you wanted pursue a relationship with me (which would be great) or not (which is also totally fine). I have always wanted to get to know you, but I also wanted to respect your family and not just jump in and throw you for a loop if you didn't know about me. I wanted to be as unintrusive as possible. You've spent your whole life without an older sister and might not want one (we can be an odd breed). If you don't, like I said, that's totally fine. I just wanted to let you know that I'm here if you do. You can write me at [address] or call me at [phone numbers].
I hope all is well with you and your family. I look forward to hearing from you.
Aimee
I think that's a beautiful letter, Aimee.
Thanks, amych.
I think I'm gonna put it on nice stationary.
I'm also terrified of a horrible, screaming phone call from one of her parents.
I'm also terrified of a horrible, screaming phone call from one of her parents.
That's part of why I suggest "warn bio-dad first". They've got nothing to scream about if he had the chance to come clean and did not.
Either way, warning him or not, I risk the phone call.
I'm also terrified of a horrible, screaming phone call from one of her parents.
Caller ID. If that doesn't work, there's always hanging up.
I'm also terrified of a horrible, screaming phone call from one of her parents.
You have call waiting Caller ID [thanks, Sparky!], right?