confusion on use of 9volt battery

I have to control two servos using Arduino and bluetooth. I have connected the 2 servos to the power and ground of the breadboard in parallel and the signal pins to the Arduino. also, i connected the ground to the ground of Arduino. but I am confused if I can use the 9v battery as an input to the breadboard and what about the Arduino do I need to power it separately.

You do need to power the servos separately from the Arduino, but it's very unlikely the servos are 9V.

Most servos work with 4.8v to 6v so a pack of 4 x AA cells would be good.

The PP3 style of 9v battery is no use for an Arduino project as it cannot provide enough current. You could power your Arduino from a pack of 6 x AA cells.

Make sure the GND of the servo power supply is connected to the Arduino GND.

...R

Budget one amp per servo unless you know the actual peak current consumption to be more. 9V batteries can supply about 0.05A without severe voltage droop, so cannot be used with servos sensibly (even if the voltage issue was dealt with).