These settings worked for me:
Install un-get on unraid - https://raw.githubusercontent.com/ich777/un-get/master/un-get.plg
Install bluez on unraid via un-get:
un-get update && un-get install bluez
Start bluetooth service:
/etc/rc.d/rc.bluetooth start
Mount /run/dbus readonly into the home assistant container
Once I did this and restarted the container, home assistant recognised the bluetooth adapter.
Note that my home assistant container runs in privileged mode (--privileged docker option). This is the default for the home assistant unraid app, but you'll likely need to mount the bluetooth USB device in if you aren't running in privileged mode. eg ---device='/dev/bus/usb/xxx/xxx'