Hey Pole, I'm not understanding wny you agreed to fly her out if she said she was flying there on her own. Perhaps to increase the likelihood she'd feel obligated to see you when she arrives?
Here is my experience with flying a girl to meet me somewhere. I always make it clear that I'll cover her airfare, plus allowance, in person with cash and nothing up front. This has worked three times.
* First was a 24yo Asian engineer chick from the Midwest who always wanted to see DC. We had never met and she was an inexperienced SB. She probably figured the worst that could happen was she had to pay for a trip she always wanted to make anyway. We met at the airport. Two nights in my hotel room and she spent the daytime hours sightseeing.
* Second was a 26yo Southern AA chick who had never been to LA. Semi-employed in theatre and entrepreneurial ventures. We had met before and she wanted me to fly her to LA when I was there. Worked out great. She got herself to my hotel. Two nights together, and she went sightseeing during the day (and did her damnedest to distract me from my work).
* Third was an 18yo, inexperienced, white chick in a small western city. Technically she did not fly to me in the large western city I was in, but she readily agreed to Uber a long distance to me with one intermediate stop, so it was similar to flying her to me because of the total distance. We had never met and she was very excited. A very sheltered girl who had never been far from her small city. Like the others, it was two nights of fucking and sucking with her entertaining herself during the day.
I've probably offered the same deal (travel reimbursement after arrival) to another five girls who declined for various and obvious reasons. But declining to pay upfront limited my exposure to ripoffs.
Most SA girls probably lack the means or desire to fly themselves to me on the promise of reimbursement. But the ones who do, really want to see me.
I travel a lot and almost have my pick of big cities in which to meet girls or fly them to. If I lived in a small town and traveled little, the calculus would be different.
Bottom line: It can work to fly a girl to you if all you offer is reimbursement, in cash, when she actually lands and presents herself to you. (Plus allowance.) It just takes the right girl and the right circumstances.