I don't know how the dating culture is in Korea, but in most European countries:
You like a girl, you ask her on a date, she's interested, she goes out with you, if things go well, you ask her again, if she's also still interested she'll keep going out with you, things should escalate by the first couple of dates (kissing, making out .. etc), if things continue to go well, then you will start seeing each other more and more.. then you'll be practically in a relationship, then you can ask her or you can both discuss to be in a relationship.
What you did is pay for a girl to travel for free in hopes that she will like you, that doesn't usually work.
You asked her to be your girlfriend although (I assume) you didn't even kiss her, people don't usually do that. I hope you didn't tell her that you loved her also...
did i bother her.
That's not a good question to ask.. If you think low about yourself and that you're someone who bothers people, other people will start thinking the same about you, even if you weren't bothering them.
If you are still in the same city, ask her out on a date, and try to kiss her at the end (or during the date if you saw an opportunity) , if she rejects you, then you will be 99% sure that she's not interested. Forget about her, and move on.