There's a variety of factors. Do you understand how big of a continent Asia is? "Asian girl" is incredibly vague. Furthermore, if she was born in the western hemisphere, even if her parents were not, odds are she is westernized and therefore having little to no difference to the average western female.
In terms suitable for the cultural layperson: just treat her with respect, bro.
Stereotypes are ridiculous. rolleyes Everyone is different. Every person. Just because 1 in a billion might act that way there are many who aren't. And as far as courting one, try real life, chatting and being friendly. Having a good sense of humor goes a long way too.