She is always busy. What should I do?

Dan4you
I have met a very kind and beautiful girl in a train station some months ago. We were close to each other, exchanged looks and eventually started to talk. Later, in the train I asked her number, which she gave me. I could tell she was happy. But when later I texted to ask her out she said she was busy. By chance, we have met 2 or 3x since then in the station and talked but she would allways be too busy. This carries on for months, despite my best attempts (and creativity). I can't tell if she likes me or is afraid to say she changed her mind and does want to go out with me. Every time she apologizes but does not give any other option, just busy. I offered to go her home town, in a weekend, where work would not be an issue here but she just gives other excuse.

Girls (and guys), what shoud I do/think about this?

It has been around 6 months... I really like her but I think I extended my patience too much.

Any advice?
She is always busy. What should I do?
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