Henry's people will meet you at the market in Chetumal, which is just a few peso's taxi ride from the bus station. They'll wait until the taxi you arrived in has departed before they show themselves though. Just tell the local taxi driver, if asked, that you're catching a bus from the market - it's a main stopping point for several.

The turf war has been declared illegal by the local authorities but it doesn't stop the local taxi drivers.

In my experience the bus ride takes five hours from Playa, and around 30 minutes from the airport to Playa. Cancun City is quite a few miles the wrong way.