bluetooth not connecting to headset

Lubuntu-18.04
I have just bought a bluetooth headset, and it doesn't connect.
It has an optional 3.5mm cable, which if I plug it into Line-out, the earphones play OK.
It also connects via bluetooth to an android device OK.
I didn't have a tray icon for bluetooth showing, but one has now appeared.
When I run blueman-manager, or whatever it is that is titled "Bluetooth Devices", Adapter and Device and all the options on the toolbar are greyed out and the list is empty.
Tray icon > Set Up New Device opens a window titled "Blueman Assistant" and says "No adapters found".
Please walk me through the basic system and diagnostics.

Updated

$ systemctl status bluetooth  
● bluetooth.service - Bluetooth service  
   Loaded: loaded (/lib/systemd/system/bluetooth.service; enabled; vendor preset  
   Active: active (running) since Thu 2019-06-27 14:32:15 AEST; 1h 45min ago  
     Docs: man:bluetoothd(8)  
 Main PID: 24506 (bluetoothd)  
   Status: "Running"  
    Tasks: 1 (limit: 4372)  
   CGroup: /system.slice/bluetooth.service  
           └─24506 /usr/lib/bluetooth/bluetoothd  

Jun 27 14:32:15 desktop systemd[1]: Starting Bluetooth service...  
Jun 27 14:32:15 desktop bluetoothd[24506]: Bluetooth daemon 5.48  
Jun 27 14:32:15 desktop systemd[1]: Started Bluetooth service.  
Jun 27 14:32:15 desktop bluetoothd[24506]: Starting SDP server  
Jun 27 14:32:15 desktop bluetoothd[24506]: Bluetooth management interface 1.14 i  
$ 

Updated

On reboot the tray icon is missing and "systemctl status bluetooth" says "Active: inactive (dead)".

"/etc/init.d/bluetooth" says "Usage: /etc/init.d/bluetooth {start|stop|restart|force-reload|status}"

"/etc/init.d/bluetooth start" says "[ ok ] Starting bluetooth (via systemctl): bluetooth.service.
$" ( that is, NOT "started").

Menu > Preferences > Bluetooth Manager says "". Subsequent attempts to launch Bluetooth Manager don't produce a window.

$ /usr/sbin/bluetoothd
D-Bus setup failed: Connection ":1.94" is not allowed to own the service "org.bluez" due to security policies in the configuration file
$

This error message is completely unhelpful without saying which security policy in which configuration file. This may go some way to explaining why there are 2,430 questions tagged "bluetooth" on AskUbuntu. I have spent 2 1/2 days trying get these headphones to work, and I'm still no further forward.