If you wish to think about electrons traveling through a circuit then you should use $V=IR$, where $V$ is the potential, $I$ is the current and $R$ is the resistance.
When you place a component, such as a flashlight bulb, into the circuit you increase the resistance. Since the voltage (potential) stays the same, the current must decrease. Yes, the current is constant throughout the circuit, but the current after the flashlight bulb is introduced is reduced throughout the circuit. In this way you can see that as energy is used to light the bulb, the flow of electrons decreases. Note: with no component, you have a short circuit and current races through the wires of the circuit generally creating a dangerous situation. As you add more components in series (along the same line) the current further decreases with each additional component with the total resistance being the sum of all the individual component's resistances.