The BASS_ATTRIB_VOL attribute is applied during playback (in the output mix) and is not present in the decoded sample data, which is what BASS_ChannelGetData/Level deal with. To make the effect of the volume level visible, you could apply it yourself, something like this...
DWORD level=BASS_ChannelGetLevel(handle); // get the sample data level
BASS_ChannelGetAttribute(handle, BASS_ATTRIB_VOL, &volume); // get the volume level
float left=LOWORD(level)*volume; // extract the left level and apply the volume
float right=HIWORD(level)*volume; // extract the right level and apply the volume
A similar thing could be done with BASS_ChannelGetData, ie. apply the volume level to the returned sample/FFT data.