If you need the streams to be perfectly in sync with each other, then you could use the BASSmix add-on to achieve that. Something like this:
mixer=BASS_Mixer_StreamCreate(freq, chans, 0); // create a mixer
BASS_Mixer_StreamAddChannel(mixer, source1, 0); // plug in a source
BASS_Mixer_StreamAddChannel(mixer, source2, 0); // and another
BASS_ChannelPlay(mixer, 0); // start the mixer
Please see the BASSmix documentation for details. Note that the sources need to be "decoding channels", which means using the BASS_STREAM_DECODE flag (eg. in BASS_StreamCreateFile calls), or not using a RECORDPROC in BASS_RecordStart calls for recording channels.