Recently I was playing around with this circuit simulation, and I found that if I had a circuit with just a lightbulb and cell, then If I were to measure the voltage between the bulb and cell it gives me 0. But when I measure the voltage between both ends of the bulb it gives me the battery voltage. If the voltage was 0 for the first one, then how do electrons even move if there is no potential difference? I'm quite confused.
In a real circuit, with a sufficiently sensitive voltmeter, you can measure a small voltage between the ends of a wire carrying current in a circuit like this. But, the wire is made of a low resistance material (commonly copper), so the voltage required to drive the current is small. This is by design.
The simulator idealizes this to zero resistance, so in simulation there is no voltage required to drive the current.
If the voltage was 0 for the first one, then how do electrons even move if there is no potential difference?
For some reason this is a very common misconception. Electrons do not require a potential difference to move. They can and do move without a potential difference or even against a potential difference.
The potential difference across a resistor is proportional to the current through it. But that is not a general law of physics. Ohm’s law specifically applies to resistors, not to other materials or devices, such as batteries, capacitors, inductors, and superconductors. For all of those other devices current can flow without or even against a potential difference.