IME, if the noise is being induced in the atmosphere (electromagnetic waves), then shielding will help, but...
All electrical noise phenomena (except DC) is electromagnetic in nature. While this is technically true, it is not always practically useful.
If you look at shielding products, you will see three different values for the shielding's effectiveness: one value for magnetic interference, one value for electrical interference, and one value for plane wave (electromagnetic) interference.
A plane wave is an electromagnetic (EM) wave in free space, and this condition only exists several wavelengths away from the EM source. This distant location is known as the far field. For radio frequencies, the wavelengths are relatively short, and so much of the radio frequency interference (RFI) that we have to deal with exists as plane waves in the far field. Thin layers of copper are very effective in shielding against RFI.
But unless your bass is picking up a ham radio communication or the top 40, we are not dealing with RFI.
So that leaves magnetic and electrical noise. The frequencies involved here are often 60 Hz and it's harmonics, 120, 240, etc. But why don't we simply treat this as a 60 Hz radio wave? And the answer is simply because the wavelength at 60 Hz is enormous. If we were far enough away from the source, we would be dealing with a plane wave; but we are not picking up a 60 Hz signal from the opposite coast of the country, but from locally right here in the room. This close location to the source is known as the near field, and in this case it is the extreme near field.
It is in this near field that we can (and should) treat magnetic and electrical noise separately. In the far field, the plane wave has a very definite relationship between the electric and magnetic fields; in the extreme near field, the relationship is extremely lopsided. So there can be a very strong 60 Hz magnetic field accompanied by a very weak electric field. Or a very strong electric field accompanied by a very weak magnetic field.
So back to the noise problem:
Single coil hum
Single coil hum is caused by strong 60 Hz (or 60 Hz harmonic) magnetic fields intersecting the pickup coil windings. Power transformers and high current power conductors are common sources of these magnetic fields. This type of noise is characterized as being highly directional. There is normally an orientation that eliminates it completely. It is also unaffected by grounding yourself by contacting the strings (or other grounded hardware).
Single coil hum cannot be shielded against without also making the pickup inoperable; anything that blocked the 60 Hz field would also block the magnetic signal from the vibrating string.
Electrical noise
This type of noise is also known as capacitively coupled or electrostaticly coupled noise. The originating source of this noise is from the various electrical wiring and devices in the room, but the most prominant source of this noise in relation to the instrument is often your own body. That is why grounding yourself by contacting the strings eliminates the noise. It eliminates the main source.
There is capacitance between yourself and the instrument wiring. You are one plate, and the wiring is the other plate. And so the noise makes it's way into the wiring by capacitive coupling. Capacitors operate on electrostatic principles, and so this is also known as electrostatic coupling.
This type of noise can be effectively shielded against with thin conductive foil or coating.
Just one more note about near field phenomenon: Imagine a short length of power ground conductor carring a heavy 60 Hz current. The magnetic field is quite large due to the large current; but the electric field is very small; there is virtually no voltage present along the length of the conductor. This is an example of the very lopsided electric/magnetic relationship I referred to. This conductor makes an extremely poor antenna, and radiates an extremely weak plane wave.
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