Unfortunately you do not tell what version/build of BS.Player you're using.
My last post in this thread is almost 14 months old!!
Since that time quite a few new features have been realized in BS.Player!
At this moment the most recent build is (version 2.57) beta build 1045.
In this build you can define (i.a.) the folder where the downloaded on-line subs should be stored.
(rightclick>) Options > Preferences > Subtitles > [Online subtitles]
"Save downloaded subtitles to ..."
(3 main options: "Movie folder, 'Subs' subfolder"//"Movie folder"//"Custom")
I think (but I'm not 500% sure) the default setting is in a 'Subs'-subfolder of the folder of the movie played.
Please have a look at the settings in your BS.Player-build.