By default, BASS will ramp-in when starting playback and ramp-out when stopping to prevent such "clicks", so you could try just stopping and waiting briefly for the ramp-out before resuming at the new position. Something like this:
BASS_ChannelStop(stream); // stop the stream
Sleep(10); // wait 10ms for ramp-out
BASS_ChannelSetPosition(stream, ...); // set new position
BASS_ChannelStart(stream); // resume
Another option is to crossfade the old and new positions using BASS_ChannelSlideAttribute, but you would need 2 streams for that: one to fade-out and one the fade-in at the same time.