The normal way to control the speed of a motor connected to an H bridge is to put a PWM signal on one of the pins. Most H bridges used with the Arduino would have 3 inputs. IN1 and IN2 which control the motor direction and braking depending on what signals are applied and an enable input onto which a PWM signal, or just 5v or GND are applied to set the speed of the motor.
So, read the pot via an analogue pin on the Arduino, use the map() function change the 0 - 1023 input to 0 - 255 (or simply divide the input by 4) and use the value in an analogWrite() command to the H bridge on a PWM pin.
Can you please provide a link to the H bridge that you are using or its circuit diagram ?