MQTT is no currently supported on bluz. We use the Particle ecosystem which uses a fundamentally different type of IoT architecture called CoAP. The two are not compatible.
There have been efforts to port MQTT to the Photon, I am not sure if it is working or not, but you can possibly use that to make it work. Ultimately, you can send down data to the bluz device through the gateway shield, so if the Photon on the Gateway shield can talk MQTT, then you can proxy messages through it to bluz using local communication.
By serial monitor, do you just mean serial output? Perhaps this will help? http://docs.bluz.io/tutorials/serial/