This bug really makes it hard to enjoy the note 3 as a whole. I was plagued by this pretty badly until recently I sort of found a workaround.
Some time ago I found out, that in offline mode the bug is not present. I came across it, when i was in our datacenter where the cell signal is a nightmare. I turned on offline mode and switched WiFi back on (thankfully we have a WiFi active there) and the battery drain was very low with active WiFi and bluetooth (headset connected) over a period of several hours.
I did still encounter the Android OS bug afterwards, but then once after my phone was fully charged, I put it into offline mode for some time (30 secs or one minute) and then switched back to normal and that day I had exceptional battery life (whole day = ~12h with some time checking, messaging and checking mail, with ~70% battery left) which i assume must be the actual battery life that the phone is capable of without bugs.
So long story short:
possible workaround for the Android OS bug: put phone in offline mode for ~1 minute, then back into normal mode
I would love to read if somebody tried this and gave some feedback.