The blue and black on the pigtail on the BD switch are for the kill/off circuit, so when you turn the switch off it closes the contact and from what I can tell the red and white w/orange are power out and power in, so when you turn the switch to off you're powering up the bike, which is what sounds like is happening.
What are the blue and green on the KTM plug going to. They should be green=ground and blue=kill. Please check that.
The BD switch has a 4 connector plug and the pigtail coming out is just the kill side, the other 2 that are not wired into the female side of the connector are for the power/on side of the switch, that's where the red and white w/stripe should be wired. When I wired mine in I added the wires into the connector, but I had all the parts because those are the connectors I wire my bike up with.
Hope that makes sense.