As anyone here knows, I read the forums here way to much, but Christ man, give a gut at least 24-hrs to get back on the ball.
Here's how I think you get the perfect diaglogue going:
U: Hey
Her: Hey
<<random discussion>>
<<conversation winding down>>
U: BTW, I'm was going to hit at Reston on Saturday, but I've got nobody to play with. You still golf?
Her: <<doesn't matter what she says>>
U: Why don't you come out and hit some balls with me <<(classic double entendre)>>
U: <<something dorky like:>> uhhh... that didn't quite come out right!
Her: <<disarmed by the dorky edge>> Sure, Great.
If she says she's busy, just drop it. If she wants to do it another time, she'll make the move and initiate.
Definitely don't use the "just me and you part" - you are in an unenviable position here of being a third wheel. You don't want to end up like Rusty Monkey!

....
Uhhh, read the rest of it... yeah I agree with Ingetral nearly 100%... it would have been better to do by chat, or, even better, by phone. Texting is pretty hard to read what's going on. And if she's picking homework over you, that's a pretty clear sign your chances that she's interested are <5%, and even if she did long distance is going to be a bitch anyway to pull off. My advice - let her go man. But if you want to pursue anything more you're going to have to be psycho circumspect about it. Like just "bump into her" somewhere random where you actually would normally be. Do you have any mutual friends? Does your school have any more games against her school? If so, then you should go with some friends...
Or, if you want to pull out all the stops, then you could get a really hot chick to go with you (if you don't know any, maybe there are some "adult dance" establishments or "escorts" near you??? get a young looking chick who can pass for 18 or it won't work... and tell make sure she knows you're going to a high school sports match/party and not S&M in your basement so she's got to dress the part... a little cleavage is all that's needed, maybe a little peak of a handlebar tatoo - but no beaver

!! and, BTW, it's probably going to cost you a couple hundred

). If anyone asks, just say you met her on a gaming site (absolutely never let anyone know she's getting paid!!). You and your companion need to both sit down close / next to Claire and Mr. Jock strap, and have your slutty chick be all flirty with Mr. Jock Strap. Afterward, you'll know pretty fast whether you have any chance in hell with Claire. Obviously there needs to be some set up (text or otherwise) to make sure Claire will be there with Jock Strap, so we're talking a significant amount of con and recon.
Again, if it were me I'd just move on!