There has been much human slaughter just south of the border. That killing is happening between various drug gangs and the government authorities. It is a low-intensity war zone. In general, they have no interest in blasting some Gringo riding a bike between Van Horn and El Paso. You will definitely not be on anyone's hit list. The main concern would be going south of the border and using the E-W highway for a while. Then, you might just happen to be somewhere when something happens such as a mass murder which has become something of a national sport in those areas. It is highly doubtful that anyone other than casual criminals might bother you. When it comes to random crime, it can happen just about anywhere anytime. If that bothers you too much, stay home. The soldiers hired on by the drug cartels have no interest in you. Don't worry about it. No problem. The same goes for the border areas from Brownsville to Van Horn. Don't go where the trouble is. It won't come looking for you.
I was teaching in Yemen for quite a while. On the surface of things all seemed calm. I had always sensed an undercurrent of coming troubles, and I mentioned it quite a few times to colleagues. Then, one day, snipers appeared and shot dead about 52 people near our school, and wounded 250 to 300 more. These murders were not random. They were committed against a certain targeted group of people. The killers did not just fire into any old group of people they came across. It's generally the same in Mexico. The killings are perpetrated against certain known and marked enemies. That doesn't include you. If I had gone to where that crowd of people had gathered in Sana'a,Yemen, I might have been killed or wounded. However, I knew to avoid demonstrations and crowds, so I stayed away from them. The moral is, stay away from the troubled areas, and you will not have any troubles. You shouldn't have any problems on the ST route in that region at all.