Disable Bluetooth discoverability in Redmi 6 / MIUI 11
Found the &quot;[Tools] MIUI Bluetooth Discovery App&quot; thread in Mi Community. It lead me to Bluetooth Visibility Fix app which seems to be working as expected under MIUI 11 / Readmi 6 phone.
There's some work when start using it:

It is a  system service that needs special permissions to auto-start,
It didn't work (&quot;restarted&quot; itself to &quot;Visible to all&quot;) for first 2-3 times then it suddenly started to work.

But after some time it does seems to be resolving the issue in question and turning off Bluetooth discoverability permanently.
In case the Bluetooth Visibility Fix app is not working for you itself, the &quot;[Tools] MIUI Bluetooth Discovery App&quot; article also mentions some user-contributed app, available as direct .apk file download under above link. Consider it as an alternative.