The ADO web site does not accept non Mexican cards. With other bus companies, it's hit and miss.
It is rarely necessary to book bus tickets in advance, except on holidays and on the top of the range long distance night buses. The easiest way to do so, if you are already in Mexico, is to book online and then select the option to pay for and collect your tickets at an Oxxo convenience store. There are probably other similar options, but that's what I have done.