Control speed of a dc motor with a 9v battery
You have 3 problems here:


Driver circuit the motor: Since you only want to control the motors speed (not changing it's direction, where you would need a H-bridge like the L298N), a very simply driver circuit is sufficient. It can consist of a bipolar transistor or a MOSFET. The Arduino's digital output pin would set the transistor/MOSFET to conductive or non-conductive, which turns the motor on or off. The motor is connected (through the transistor/MOSFET) with the full supply voltage. For the needed circuit, you can google terms like "transistor as switch" or "MOSFET as switch". That should give you plenty of tutorials.
Controlling the motor speed: Normally the speed of a motor is not controlled through the voltage, since the speed behaves not linear with the voltage. Instead we use PWM (Pulse Width Modulation), where a squarewave voltage with a constant frequency is outputted at the Arduino's pin. To change the motor speed, you change the ratio between ON and OFF time of the pin (called "duty cycle"). So the motor basically get's turned on and off very fast. Since the motor is to slow, to follow the fast change, we are basically giving it small pushes very fast. If you only push half of the time (duty cycle 50%), the motor will run with about half the speed. In Arduino code you use analogWrite(pin_number, x) with x between 0 and 255 to output a PWM wave at the specified pin. Refer to the Arduino documentation for details.
Powering the whole device: First: A 9V block battery is actually like the worst choice for most cases (especially for devices with motors). It has a big series resistance, what means, that it cannot provide much current without dropping the voltage radically. They are meant for low-current devices. Better use multiple AA/AAA batteries in series.

You didn't state, what Arduino you actually use, but from the description, it has to be one of the 3.3V boards, like the Arduino Pro Mini 3.3V version. Most Arduino boards also have a small voltage regulator on them. The input for it is mostly marked with Vin. Please refer to the documentation of your Arduino board, to check, which voltages are suitable for that voltage regulator. If you don't have a voltage regulator on your Arduino or your battery voltage doesn't fit, you have to provide the power through your own external voltage regulator. You should use a switching regulator (far more efficient, than linear regulators), which can provide the needed power (depending on the Arduino and the bluetooth device maybe between 50mA and 300mA, difficult to say generally) plus a bit overhead.

You should then provide the motor with the full battery voltage, especially not through the Arduino's voltage regulator. Motors can draw quite much current. If you draw more current through a regulator, than possible, it will overheat, emergency shutdown or even burn out. If the battery voltage is not suitable, you should use a voltage regulator, that can safely provide the needed current.




Note: Depending on the size of the motor and it's load, you might want to add a flyback diode, that would safely let inductive reverse currents flow to ground, so that the inductive voltage is not piling up in the transistor/MOSFET.