I had found so far two ways to make the programmatically delete the Bluetooth recent history list.
Solution 1: (That works) Is to run the command pm clear com.android.bluetooth
Solution 2: (Requires more work)
I am trying to use in Android Manifest:
<uses-permission android:name="android.permission.ACCESS_BLUETOOTH_SHARE" />
And in the Java code:
getApplicationContext().getContentResolver().delete(Uri.parse("content://com.android.bluetooth.opp/btopp"), null, null);
And
getApplicationContext().getContentResolver().delete(Uri.parse("content://com.android.bluetooth.opp/btopp3"), null, null);