I just completed a 350 mile off-road border tour over the winter holiday that had me within 10 miles of the border basically the entire time. This was the region of HIGHEST density crossing for drugs, humans, etc. along the entire border with Mexico. (Between BANWR and New Mexico in S.E. Arizona.) People thought I was crazy for getting that close to another country without a .45 on my waist. (fear and xenophobia is strong these days...)

Exactly Zero problems, I was woken up by a Border patrol helicopter that had its searchlight on my tent though... When they saw I was just a pinche gringo on a bicycle they left me alone, just like everyone else did. I heard 'crossers' come through my camp at night, which is not unusual for this area, but they too just passed through, not wanting to cause trouble.

Maybe consider crossing the border further west and riding down Baja California? Just a thought. youll be fine, and as soon as you pass the border zone where the trouble is, youll be in one of the friendliest countries I know of.