The three-way pickup switch in my PRS CE has been popping lately, I'm not sure why. What resistor values should I use to stop this and how should I configure them to this particular switch? thanks.

it might be popping if the first thing it's plugged into has dc leakage on the input section.  measure the instantaneous dc level with a good meter by leaving the cord plugged into your first effect (or whatever your guitar plugs into) and checking the dc level from tip to ground.  to get fast response on your meter, put it in manual range select mode and select a range of just a few volts.  if you see it show voltage for a moment when you connect the meter, that may be the source of your trouble... dc leakage through your guitar's cord can cause the pickup switch to make noise.

adding bleeder resistors to a circuit that is basically all resistors and inductors (the pickups) isn't going to stop popping noises... there's no dc inside a passive guitar.

That all makes sense, but then what would I need to do to fix the DC leakage problem in that particular effect (one instance was with a recently completed GGG Mod Wah that I was testing)?

Add a cap to stop the DC. You should do it on the effect's input and NOT the guitar. Otherwise (since most effects have an input cap) you'll be putting two caps in series, decreasing the capacitance and you'd lose all your base.

Seems a pulldown resistor just before the input cap to ground might help?