The written case which Vlad talks about is actually given at Final Round interviews, so comparing it to the PST is not particularly helpful.
You are right - Bain does not have a pre-interview problem solving test which is rolled out globally. However, local offices have started experimenting with their own "PST-like" versions - for example, our Africa offices are doing this. In other offices (e.g. London), Bain only currently uses a pre-screen quant/verbal test (think CEB SHL test, which you can find lots of examples online).
Hope this clears some things up!