^^This.
It would be different if you were in an ongoing relationship like
@BeExcellent scenario, but here you met her briefly on vacation, you're not dating, you haven't even f*ck ed. Or have you? You never responded to that question.
There is also the safety issue of her staying with a man she barely knows. Not smart.
You invited her; be a gentleman. She's paying for the flight which given the distance is not cheap!
If you end up really clicking and the sexual energy is there, she could always check out of hotel early and stay with you.
But expecting that she stay with you right off the bat? A woman who barely knows you?
Or that she pay for her flight
and hotel?
I think that's a bit much to expect.