Hi FJ,
I don't think it's common for a Polish girl to date several different guys at the same time. If she's a PhD student, she surely must be busy (she's probably working and studying at the same time, isn't she?). I think she told you she had a boyfriend just because she was... too busy and didn't have time or didn't feel like going out with you at that time. Polish people (especially those who live abroad and try to work and study) are pretty ambitious so if she thinks she won't be able to manage both professional and personal life, that was probably the reason she didn't choose to get to know you.
Also, I feel asking this straightforward question: "Do you have a boyfriend" is not a good idea. Some Polish girls like to be won by frankness, maybe sense of humor or politeness. When you asked this direct question, she might have felt you like to choose the easy route and she deserves something more. Maybe try to share your interest with her, suggest to show her an interesting place -- not ask this question rightaway...
In true love there are no shortcuts; if this is to be a long-term relationship, it needs to be well-prepared. Rush doesn't help true love!

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If you really care about her, don't give up, but be a little more inventive.
Cheers,
Gosia