If you use non-metallic wiremold and a non-metallic box, then 250.86 is moot, as there are no metallic raceways or enclosures involved.
If your receptacle behind the bed does not have an EGC, then it should be a 2 prong receptacle, unless you either (a) comply with 250.130(C) to provide an EGC or (b) comply with 406.4(D).
Since 406.4(D) only discusses receptacle replacement, I believe you are not allowed to extend an ungrounded circuit without complying with 250.130(C) to turn it into a grounded circuit. Edit: Often complying with 250.130(C) is no easier than running a new grounded circuit to the area, which is then a better solution.
Cheers, Wayne