My best guess is that the signal bleed must be coming from the bypass switch. You always have input signal coming from the tip of the input jack, to lug 4 of the bypass switch, and over to lug 9 of the bypass switch. Lug 8 is the output. So, I'm guessing that signal is bleeding from that input signal path (probably from the jumper from lug 4 to lug 9) onto the output wire.
My first thought would be to replace the output wire (bypass switch lug 8 to the tip of the output jack) with a shielded wire. Here's a tutorial:
http://www.olcircuits.com/documents/olc_shieldedwire_guide.pdf I ground the shield at the ground lug on the output jack. If that doesn't do, shield the input wire, and re-route the jumper from lug 4 to 9 making it go around the base of the switch instead of between the lugs.