Penny de Valk's Answer:
Your decision to speak to her one-to-one is a good one. You don't need to specifically refer to your cultural differences but to be cognisant of them when you are speaking to her. In fact it is an opportunity for you to demonstrate your sensitivity to these differences without being overt about it.
You will be aware that these 'direct' conversations may seem quite challenging but if done in a conciliatory way using language like "when you...I feel..." as opposed to "you are being rude and dismissive etc" might get to the bottom of what her problem is, recognising that she is unlikely to tell you directly if she has a problem with what you are doing.
Instead try to understand her motives by asking open questions about how you might enable her success, checking in with her about her own career aspirations and what suggestions she has for how things could be improved - it might uncover what she is trying to 'prove'.
Good luck with the meeting and in your career generally - it is a real challenge trying to be an effective manager outside of our cultural milieu but an important one for managers to embark on. You are a pioneer and that is not always an easy role to play!
Penny's advice is a very western approach to a Chinese problem. Its success depends on western responses to the ‘... when you... I feel..' stuff.
You may not get the responses that you are expecting as the Chinese have a different culture than you. [No kidding, really?]
I would hope that you have done, and are still doing your homework and are 'getting into' the Chinese psyche. Only by knowing this will you discover why the person is doing this and more importantly to you, how to combat it.
I am currently working in Moscow and that warm style of management is looked upon as weak here and any attempt to use it will lower your status in the eyes of Russian men. [and put you in an even worse position than you originally were]
So, study the Chinese way, think about motivations for her behaviour, test your theories with small exchanges and when you believe that you have her motivation, think about a Chinese way of overcoming it.
Have fun as this is the enjoyable part of expat management. :-)
Just came across this & thought I'd add my two cents worth although of course it is from 2008 & now we are in 2010 & the situation may be well resolved by now! As part of your cultural homework and lived experience you will have learned that the comms style in China is indirect. Third parties are used a lot. The whole team is probably aware of what is really eating this person. Which 3rd parties might you go to to help you understand the situation better? And/or convey a message thru a 3rd party as well. This saves face all around and may be a good starting point to have better 1:1 dialogue. Hope this helps!