The simplest way to do that is with the BASSmix add-on's "splitter stream" feature, which allows you to extract specific channels. For example, something like this...
source=BASS_StreamCreateFile(FALSE, filename, 0, 0, BASS_STREAM_DECODE); // create a decoder for the audio file
int chanmap[2]={channelindex, -1}; // channel map to extract the wanted channel
split=BASS_Split_StreamCreate(source, 0, chanmap); // create a splitter stream using the decoder and channel map
BASS_ChannelPlay(split, FALSE); // start it
Please see the BASS_Split_StreamCreate documentation for details.