I would say: I met her when I first visited China. She had been studying there for a few month at that time.

1- Past perfect continuous (had been studying) describes a event in the past that happened before another past event during a certain period of time. In those phrases the time mark is the moment of the meeting and before that for a few months she has been studying. 2- Past continuous (was studying) describes an action uncompleted in the past. In general, it comes followed by the simple past, for example, "I was studying when she phoned me". The action 'to study' was interrupted by the action 'to phone'. So, if you use the second phrase it lets open to understand the she did not complete her studies and it maybe because you met her.

Hi Илья! Your first option is the most natural one. Just a few things: 1. She'd been studying in China - 'to'+a place is pretty much only used when talking about movement in a specific direction or with the verb to be in the present perfect or the past perfect in constructions such as "I've been to Paris twice". 2. 'By that moment' and 'at that moment' both are fine, but they convey slightly different ideas. 'By' means 'no later than' and 'at' means 'at that precise moment'. The difference is very small. 'By' just emphasizes how long she's been in China more. 3. In the phrase 'For a few months', just remember to add the -s to months, since 'a few' is always followed by the plural. Hope this helps! If you have any questions, please don't hesitate to ask!