There's more than one way to wind a bifilar coil. An example which often comes to mind is Tesla's pancake coil. He wound a flat coil, with two side by side wires spiraling outwards from the center. When finished, the inner end of the second wire was brought out and connected to the outer end of the first wire. Then the outer end of the second wire, together with the inner end of the first wire formed the coil's two leads.
This same system can be applied to a solenoid coil having two layers. The end of the inner layer is brought back to the starting end, for the beginning of the second layer. So the starting end of the inner layer, together with the far end of the outer layer comprise the two leads.
(http://s20.postimg.org/whalr0mlp/Tesla_Solenoid_Choke.jpg)
It can be seen that this is equivalent to using speaker wire to wrap Tesla's pancake coil, with the two layers stacked. Doubling up on the two layer coils can provide a choke, depending on how the twin, two layer solenoid coils are connected to each other.