Wow Merida. Dont know much about that place other than it's pretty different from the rest of the entire country. I dont think it's got any particular problem with violent crime though.
The capital is a different story. Like I said, educate yourself about the different areas of the city before you go. If you're there on business I expect you wont have any reason to go into the really dangerous areas though. In some ways it's similar to DC....it's the seat of the government, but it's also got some seriously bad neighborhoods.
Just dont be foolish and attract a lot of attention to the fact that you may have a lot of cash. Be very polite with the police if you get hassled. And interstate bus travel might not the best option for you. Fly from Merida to the capital in you can.
Most of the people are really very honest and decent, but being American everyone will see you as being rich and you will attract the scumbags. Sorry.