Hello,
I would like to create a project contains 6-8 servo motors , HC-05 Bluetooth module and Arduino Due board, but I have no idea how to operate should I use only a 9V battery only or in addition to 4 AAA battery?

And how to connect them ?

 

9 volt one of these

Will not last long go with the 4 AAA batteries

 

9 volt one of these

Will not last long go with the 4 AAA batteries

Could please show me how can i connect them together "circuit design "

 

I'd go for another power source. From this link: Arduino Duo it says

Input Voltage (recommended) 7-12V
Input Voltage (limits) 6-16V

I'd find something near the recommended values, considering the bluetooth, and the servos.

 

The 9 volt is not going to work and need to see more about what you have what shield your going to use.