You do not have to wrap the bonding wre around at all.

You can just cut off flush before installing the required anti-short bushing (for type AC).

They anti short bushings are usually the little red split sleeves.

They go between the wires and the armor.

Be sure to use the correct cable clamps for type AC.

NM clamps are NOT correct.

The bonding conductor is only there to ensure a continuous ground from the armor (the grounding conductor for type AC cable).

Only one wire can be under a screw head, and you will need to use the hole in the box for the NM grounding conductor.

You must use a metal box with type AC.

Brickeyee,

I was under the impression that with AC the bonding strip was folded back along the armored jacket and essentially "captured" by the clamp, not cut flush at the end of the jacket.

Leslie,

Early on armored jacket of functioned as the grounding conductor but over the years they've determined that the ability of the jacket alone to function as the grounding conductor was insufficient so they added a small strip of aluminum to augment the current carrying capacity of the jacket. The rules say that the bonding conductor is not to enter the box.

I'm sure that Brickeyee will chime in here but I'm, too, curious what would happen in a fault if the bonding conductor was tied to the box.

Brickeyee is correct in that NM (aka Romex) clamps look very much like AC clamps but they are not interchangeable. Make sure you use the correct clamps.

Mike:

It is NOT necessary to do anything with the bonding strip. It's OK, to do what you want, but what brick suggests is perfoectly acceptable. This explanatory text is in the NEC handbook:

The armor of Type AC cable is recognized as an equipment grounding conductor by 250.118, and the internal bonding strip required by 320.100 can simply be cut off at the termination of the armored cable, or it can be bent back on the armor. It is not necessary to connect it to an equipment grounding terminal. It reduces the inductive reactance of the spiral armor and increases the armor's effectiveness as an equipment ground. Many installers use this strip to help prevent the insulating (anti-short) bushing required by 320.40 (the "red head") from falling out during rough wiring.

Thanks for the replies but my question hasn't been answered.
NEC says,"It is not necessary" to connect it to an equipment grounding terminal
"not necessary" translates to "do it if you want to"
But from what I read the text was emphatic in saying "NOT" to connect it to the grounding terminal.
Along with mike i'm curious as to what would happen in a fault if the conductor was attached to the box.

""not necessary" translates to "do it if you want to" "

It is a waste of time, and yuo can only have a single wire under a screw head.

It is also not going to mix well in a wire nut since it is small and aluminum.