PyBitmessage can be run in deamon mode by adding this line to your keys.dat file under [bitmessagesettings]:
daemon = true
In this mode, PyBitmessage doesn't require Qt. You will then need the API. If you do not yet have a keys.dat file because you have not yet run Bitmessage, run it. It will create the keys.dat file for you then exit if it cannot find PyQt.
The client can only be controlled via the API, so it is important to set the API values too in the keys.dat file.
Example Daemon for using Bitmessage via a console: Bitmessage Daemon (GitHub)
Running with an initscript on Debian-based distros
You can use an initscript to have the system automatically start bitmessage at boot. For more information and a basic init-script, look here: Bitmessage-Init (Github)