I'm not sure if the dual citizenship thing will change this, but . . .
If you ride the bike into the hassle free zone (Sonora & baja) - no importation is required. But, if you are towing (including hitch carriers), you have to import each 'vehicle' (one permit listing each VIN). I've never done it, but I have heard that if you ship a vehicle down, you will have to do the temp. vehicle import on it (so that last bit is 2nd hand info - take it as such).
If you're going outside of the hassle free zone (Sonora & Baja), you need the temp import permit regardless.
"Life is meant to be enjoyed, not endured" ~someone