From downtown Cancun: If you are in downtown Cancun you can choose to take the ADO bus, but as such this bus does not include Akumal as one of its transfer destinations. However, being close to the city of Tulum, it allows you to have the "drop off" on the federal highway where Akumal begins.
Another much more economical option is the public service that consists of two units: Playa Express and Transporte foraneo de Tulum. First you have to take the Playa Express unit in downtown Cancun which will take you to Playa del Carmen and in Playa del Carmen, take the public transportation to Tulum.
Since "Akumal" is close to Tulum you can get off at the federal highway and walk to town. Of course, you can also request our private cab service to pick you up in the center of town and take you to Akumal,
From Cancun airport: Transportation from Cancun airport to Akumal must be private. It is not as such an obligation but, from Cancun airport you can take the ADO bus to Tulum and in this case, if it is strictly necessary to get to the center of Tulum.
Therefore, you in Tulum will have to take a bus or cab to akumal. On the other hand, cab services from the airport cannot take you to Akumal because they do not have federal licenses and travelers insurance.
If you want to "economize" your departure from "Cancun Airport to Akumal", you could take the ADO to get to downtown Cancun and from there take other cheaper transportation,
