Yes, it's better not to wait too long.
How to ask is really about first deciding what you want to do. Are you going to drive back and forth in the same evening?
See if you can get her to invest somehow in the meeting.
Booking a cheap accommodation and asking her to meet you there would be my first option. It has worked many times for me in the past (see
my latest LR, but also several times before in late 2015). There are many things playing in your favor, one of them being "the Prince from afar" fantasy shared by every girl. Plus, she is investing in it, merely by coming to meet you. And last, you have readily available logistics at hand.
In any case, I don't recommend a "fun date" (cinema, meeting friends, bowling etc...) which is not supportive of seduction. And to be avoided, the dreaded formal dinner, or otherwise formal date. It should be a low pressure date, not too noisy, not much people around, and no big deal thing.
Whatever you decide to do, be aware that, once you agreed on the details of your meeting, she is likely to test your frame by trying last minute changes to agreed deal. It is so very typical... Things including "I'm coming up with a friend" or "I have a party coming up, just join me" popping at the last minute, once you already agreed the date. It's a test. The approach is to stand firm on what was agreed initially. "No. It's a date. You and me only". If you stand firm on your frame, you earn points. If you bow to her frame, you lose many points. As always, better to lose the girl than losing the frame.
But that's jumping ahead
Keep us posted.
Seppuku