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Shielding - How do you know it will help?

Right on. The copper foil is sold as having conductive adhesive, but a quick check with an ohmmeter shows that to be optimistic. Spot-soldering adjacent pieces is a wise approach.

I agree - optimistic indeed!

The shielding folk build inside their basses needs to be as low an impedance as possible. Ideally it wants to be made of solid, seamless copper. But, as that is not possible, we need to emulate seamless copper, and the easiest way is to blob solder at very frequent intervals along every single seam / adjacent pieces of foil. The more solder blobs you put on the more likely you we to have an improvement in the screening.

If (say) two pickup cavities are shielded I run a wire from each to a point nearest the jack socket earth connection to achieve the star earth arrangement I mentioned in a previous post. The cavities **are not** joined to each other electrically, there and then: their common connection is the star earth point. In fact, as a matter of course, I make all ground points and signal screened cables (eg. pickup wires) to the star earth point.

RJ
 
By the way, the spray-on SuperShield Nickel (or Copper) shielding is very low resistance. I spray on two coats in the cavities of my basses, and I read 1 ohm or less across any two points anywhere. That's equal to or better than well-installed copper tape. And spraying on more than two coats doesn't make the resistance go significantly lower.
 
The embossed copper tape made by 3M with conductive adhesive does work.
You can get better than 100dB of shielding from 1K to 10 gHz all day long.
The embossed tape does not have adhesive on the embossing plus the adhesive is conductive.
The nickel paint is easy but not nearly as good as the proper shielding tape
I tested some silver paint years ago in an RF shielded chamber.
The test panel was 18"x18"
This stuff was about $250 a pint in the 80's and was just OK.

I worked exclusively in RF shielding (and acoustic attenuation) for nearly 15 years.
Something that just occurred to me.
I have 4 P Basses and none of them have shielding tape although 60' does have the aluminum plate behind the guard.
The 70's basses have that small piece of aluminum tape at the pot cavity which probably does very little.
I have a J bass with Dimarzio's and it's dead quiet as well.

My Spector has shielding paint and I suspect it might need it due to the preamp.

If you really want to shield a bass just for fun, use a metal pickguard, conductive tape the cavities, and good humbuckers.
IMO, other than radio stations, the noise you usually hear is 60 cycle off the powerline.
Most amps have filtered power supplies and using an outboard filter does nothing until you get into high dollar units and even that is marginal. (I did use a powerline filter on an old furnace condensate pump but that was because the pump was junk. A new pump solved that problem)
While I can't explain it, I have seen shielding help to a limited degree with 60 cycle hum.

BY the way, 60 Hz is well below the "E" field which means that if you were truly trying to filter an RF signal at 60 hZ, you would be in the "H" field or magnetic field.
It takes ferrous metal to isolate this but not a big deal as the amplitude of the signal drops like a rock with distance.
Walk up to a TV with your bass plugged in and it will scream like a banshee. Move back a few feet and problem solved.
 
Ok .....here's my $0.02

It is my understanding that noise in a circuit is created by current running in loops in the ground. Generally speaking, the larger the loop, the greater the noise.
Making the ground loops smaller will reduce noise, as we see when we shield the cavities of our instruments. It's not that the shielding is acting as a Faraday cage as much as it is breaking the ground in smaller loops
 
Noise is caused by induction in the pickup windings.
A ground loop occurs due to two or more devices having a ground connection at different potentials.
That pretty much sums it up! The pickups and connecting wires receive electromagnetic waves from poorly shielded mains equipment such as lights and convert them to a tiny voltage/alternating current at 50-60Hz, although the fundamental at 50-60Hz (between low G and B) is barely audible - what you are mostly hearing is the higher order harmonics generated, so you actually hear more of a 'buzz'. To deal with this you build a Faraday SHIELD (not cage) i.e. a complete metal shield around every orifice of your guitar/bass, as far as possible, and connect it to ground. You don't have to solder it - as long as one point of a completely integral shield makes good contact with an existing ground point on the same circuit as all ground connections, it should work. I used aluminium foil for my Rick (was a noisy beast!) and it works really well.
 
We can have both types of hum pickup - inducted hum into the windings and cables, and also from ground loops that make tuned antennas. The ground loop issue is why cavities and control plates should be grounded ONLY at a single point, and the theory behind star grounding. Our runs are so short that anything picked up from a 4" ground loop is probably inaudible, but it doesn't hurt to be careful!

I have had only good luck from using Copper foil with conductive adhesive from Stew-Mac. The first time I used it, the bass was so quiet that I thought I had shorted the output!

Don't forget to twist the wires from the pickups a few times to get a little common-mode rejection as well.
 
This is how I shield my basses.
Boss NS-2.jpg

I set it to Mute, so I can stomp on it and kill the signal from my bass for between sets, Threshold at 3 o'clock and Decay at 9 o'clock. Works great, and no messing around with tape or paint. I stop playing and it kills the noise instantly!
 
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Right on. The copper foil is sold as having conductive adhesive, but a quick check with an ohmmeter shows that to be optimistic. Spot-soldering adjacent pieces is a wise approach.
I don’t know, on the bass I just finished building a couple months ago, I used foil, and the only solder points I have are where I connected the ground wire. I have consistent conductivity between all discrete pieces of foil, due only to the adhesive. I must get a good brand of foil.
 
Now, why does Fender only shield the p/u cavities in their Mustang basses? How much more expensive would it be to properly shield under the control plate and where the 3-way switch sits?

I think this falls under the if it isn't broken...
Can't remember ever playing and American made Fender P that ever had a shielding issue (60 Hz.)
If there is no issue, adding conductive adhesive copper tape offers no advantage and adds build cost
Sounds like most here are talking about 60 Hz noise and not RF issues or dirty power