Oh, I see. With ASIO, you would join 6 mono ASIO channels using BASS_ASIO_ChannelJoin (enable 1 channel and join 5 others to it). With WASAPI, you would set the BASS_WASAPI_Init "chans" parameter to 6. You can then call BASS_ChannelGetData on the 6 channel stream (created with the BASS_STREAM_DECODE flag) in your ASIOPROC or WASAPIPROC callback function. You don't need to do anything special in your BASS_Init call, but you could use the "no sound" device.
One thing to note is that the ASIO driver may have a different channel/speaker order, and you may need to swap the rear and cen/lfe channels around. The easiest way to do that is using the BASSmix add-on's splitter stream feature and its "chanmap" option. For example, like this...
int chanmap[]={0, 1, 4, 5, 2, 3, -1}; // channel mapping to swap rear and cen/lfe channels
split=BASS_Split_StreamCreate(source, BASS_STREAM_DECODE, chanmap); // create the splitter stream
You would then use the "split" handle in the ASIOPROC's BASS_ChannelGetData call.