Some people have suggested that you are unlikely to be targeted because the the violence is mostly drug-related and limited to the border. That is true to a certain extent, but you are still taking a real risk. Consider, for instance, that Mexico has a lot of kidnapping for ransom. The problem is not limited to the border, and a foreign bicyclist might make a tempting target.

See:
http://www.nytimes.com/2009/01/05/wo...appings&st=cse
http://www.nytimes.com/2008/12/16/wo...appings&st=cse

Even if the chances of something terrible happening to you in Mexico are low in absolute terms, you'd be kidding yourself to think Mexico isn't MUCH more dangerous than the US.