1 month before I will board my expensive across-the-globe flight (US$1,000), she proposed an open relationship, reason being that I don't make enough time for her and if, only when it is convenient to me. We haven't talked for a week now, but I offered her to talk to me whenever she is ready.

It is three weeks until I fly to visit her, but if she doesn't reply, it seems that I will just chill by myself in fucking Hong Kong. I believe the timing is really fucked up. What do you guys think?

it all depends, if you really love the girl, then you will have to put more interest in your relationship, if you are a player or you are not really interested on the girl then you can see the offer of an open relationship as a hall pass and reap the benefits of it plus the benefit of having your girl in the whole package.

She's not wanting an open relationship. She's 'protesting' a desire to spend more time together, and the open relationship suggestion is being used out of desperation to have her need met. Some empathy may get you in the ballpark of preventing a rift, some re-assurance that you'll make effort to remain in contact during your trip may also help alleviate her fears.

Her behaviour exhibits a fear of a loss of attachment (most likely). If the relationship is important enough to you, learn to hear the need beneath her words and you'll be in a far better position to use these opportunities to grow closer rather than apart.

You have a point. I have told her that many times, but she says I never listen (which is probably true to be fair)

I still haven't heard from her. Should I text her or wait for her to text me? (considering that I already reached out, but she was kind of cold) - I dont want to blow it, dont want to lose her, but I will also not bend for a relationship on her terms.

If you care about her transparency and openness in communication are key to establishing trust, security, and overall a healthy bond.

"bend for a relationship" can easily be reframed as she's potentially hurting and not feeling as though she has a voice. Its win win reaching out. You can diffuse the situation and re-connect, or if she maintains the open relationship thing then you can decide how you want to navigate forward whether with her or find someone else who is in more alignment w your needs.