My take on it:
The physics of it is simple, most of the time, when we are focussed on something far away, the distance between the lens and the film is approximately the focal length of the lens, and the image circle is about the same size. When you start to focus on something that is very close, and now the lens is further away, and the light that it is gathering is spread over a bigger image circle, so we have to increase exposure to compensate. Most of the time, you don't have to worry and you can ignore the bellows factor.
When do we need to start worrying?
1) with B&W film, I usually overexpose some, so I feel that I can tolerate 1 stop of underexposure before I start running into problems - I get one stop of underexposure when the image circle is twice the area as it is at infinity - which means that the diameter is a factor of SQRT(2) - or about 1.4 larger. The image circle diameter is proportional to the lens to film distance, so if I set up my camera for a close up and the lens - film distance is more than about 1.4 X the focal length (eg with a 150mm lens, 210mm) then I go through the calculations and adjust my exposure - or more likely, I toss in a seat of the pants adjustment. If the distance is 1.4X the focal length, I add one stop of exposure, at 2X the focal length, 2 stops, etc.
2) With color film, (transparency) I am more sensitive to exposure, and I get out the calculator to work out the exact right exposure with the equations.....
The other way to do it is to move to a camera with a built in meter, where you can meter off of the ground glass, and then it is all taken care of automagically for you.