It is possible to get notified when a device fails (eg. is disconnected) via a BASS_SYNC_DEV_FAIL sync set on a channel on the device. The channel doesn't need to be playing for the sync to be triggered, but BASS does need to be playing something on the device or BASS_CONFIG_DEV_NONSTOP enabled.
Another option is to use the BASSWASAPI add-on's BASS_WASAPI_SetNotify function to request notification of when devices are enabled or disabled. You can still use normal BASS output then, ie. you could use BASSWASAPI just for the device notifications.