Potentiometers, as they're used in instruments, are not just variable resistors. The middle pin on a potentiometer is called the Wiper. It's potential (Voltage) varies between that of the other 2 pins, but if the Wiper is the source, the other 2 pins vary with the wiper. Typically, Pin 1 is Ground, Pin 2 is the (+) lead of the Pickup, and Pin 3 is the output. As the potentiometer turns, the resistance decreases in one direction, and increases in another. For example, if you have a linear taper 500K potentiometer, with Pin 1 grounded, Pin 2 connected to the pickup, and Pin 3 connected to the output jack, when the volume is all the way down, the resistance between Pin 1 and Pin 2 is 0, and between Pin 2 and Pin 3 is 500kOhms. This is oversimplifying it, but electricity tends to travel the path of least resistance. So all of the pickup output goes to ground. When the volume is halfway, the resistance is the same, 250K, between Pin 2 and 1, and 2 and 3. So the output is split. When the volume is wide open, the resistance between 2 and 3 is 0, and between 1 and 2, it's 500kOhms.
This is not a realistic example, as volume pots are not linear taper, but logarithmic, it's just a simple example to help understand how potentiometers work.
But as for how the sound changes when both pickups are on vs when 1 of them is on, obviously each pickup 'feels' different frequencies, but I think what you're talking about is how the neck pickup can have more bass by itself than with both pickups on. This has to do with phase cancellation, I would think. Think of vibration as pushing and pulling. When a string is plucked regularly, the whole string pushes and pulls together, like a jump rope. This is not the case with harmonics, so I'll leave that one alone for now. But basically, the whole string moves to one side, then to the other side, and back again. The bridge pickup 'feels' the string pull to one side, and translates that into an electrical signal, as does the neck pickup. But due to their different locations, different windings, different wires, etc, when the signals are combined at the output, the translated pushing and pulling is not synchronized for all the frequencies. They're not completely out of phase, if they were, there wouldn't be any output, but they're out of phase just enough so that certain frequencies are empasized while others are de-emphasized.