Mexico is a big country made up of 31 states plus the federal district, and the security situation varies enormously from state to state. I've biked in the Yucatan peninsula and Chiapas, and they are generally quite safe. So are the states of Oaxaca and Puebla insofar as cartel problems are concerned. I traveled in both of those states 2 years ago, but not by bike. Among states near Mexico City, Guerrero and Morelos have significant security problems.