If she doesn't already have travel considerations outlined on her site, it's a gray area and tricky to discuss. But don't be too concerned how she'll react if you offer a rate that's too low -- if instead you asked how she'd like to be compensated, she'll be just as concerned about offending you with an offer that's too high.
Remember when discussing compensation, while it will be something of a vacation for her (especially with all the free time during the day), she will be entertaining and stayin' pretty and being a convincingly innocent and charming dinner guest for you. That can take a lot of effort. Also, while she's out of the States, she'll miss any provider income she'd otherwise be getting -- AND she may need to get child care/a pet sitter/take unpaid time off a day job/etc., depending on her situation. A spur of the moment vacation is lovely, but not all of us can afford to do so even when all the hotel/flight/meal costs are covered.
I think the first step would be to see, first, if she'd be interested and even able to go abroad -- the first two logistics Lust4xxxLife mentioned are especially important. Then, one of you has to get the ball rolling with the compensation discussion. If she doesn't offer an amount, it's up to you. If she has an overnight, day, or "clock free" rate, consider that as a starting point for your per diem and you can both negotiate from there.
As an aside, if you haven't yet, I'd suggest having an overnight together in town well prior to hopping the pond, to make sure you actually *are* still compatible after several hours of each others' company. You don't want to be almost killing each other after only the flight over...