I agree it would be a bad idea to use only red light for the bike ride, but why would red light be a problem for taking notes unless you were using red ink or red-lined paper?
If the light is one of the common red lights that's used for night vision purposes, she will be able to use it adequately for things like note taking. The problem with this is that those kinds of lights have their output in the 620 nm range of wavelengths, which is still in the range of the cone receptors, and if they are active, dark adaptation cannot take place. A true night vision red light should be what's called a 'deep' red, in the range of 670 nm or so. This is far enough up the visible spectrum that the cone receptors, specifically the long wavelength or red receptors, will only be activated a very little at this wavelength, and allow true dark adaptation to take place.
When true dark adaptation occurs, the cones are shut down, they don't send any signals to the brain because there isn't enough light to activate them. However, the rods are still sensitive at these much lower levels of light. This is what's known as scotopic vision, based only on the rod receptors. All high acuity vision, which is what's necessary to be able to read or see small details occurs only in the cone system, and only in the fovea, the center of the retina. It's the spot in the retina that directly corresponds to what is right in front of our eyes, what we're looking directly at. So, when truly dark adapted, high acuity vision is impossible, so she wouldn't be able to take notes, read, etc. because she has no acuity in her visual input.
An NVG light on the other hand, is at a wavelength around 500 nm, which is in the green/cyan range. This is the frequency at which the rods respond best. The green cones also respond here, so keeping an NVG light at a low level is crucial to maintain scotopic vision. When using an NVG light, it can be set at a level where the observer is at the cusp between the photopic/scotopic break point. The cones can be activated very slightly and high acuity vision is possible, while still maintaining true dark adaptation.
In either case, there is a simple rule to know if your light is too bright or the wrong wavelength for true dark adaptation. If you can see the color of the light, it's too bright; you are activating the cones and cannot go into full dark adaptation. This is true for either red or green lights because the rod system, which provides scotopic vision, is color blind, it does not send any signals to the part of the brain where color is processed. All light looks the same to rods, the only difference is its intensity. Light that is out of their range of response wavelengths isn't seen anyway.
That's why I say that for true dark adaptation, using a red light prohibits you from doing things like reading and/or taking notes.