Unfortunately, public transportation is generally not considered a viable option for travelers visiting Cozumel.  There is a public bus system in Cozumel, but it does not go to either the hotels or the beaches which are the two main areas between which visitors are likely to travel.  However; visitors interested in getting from one place to another within the town itself, particularly in the downtown area, might find that the bus in Cozumel works for them. Route maps are available at http://everythingcozumel.com/Maps.html

Preferable to busses are taxis.  Taxi fares are standardized by the union operating in Cozumel, so be wary of any taxi driver who tries to charge you additional fees or to bargain with you about cost.  Standard taxi fares should average about $5 to town from the hotels north of town, $10 to town from the hotels south of town and $60 for an all-island tour.

For visitors interested in finding out about public transportation between Cozumel and the mainland, the best way to go is the ferry.  The ferry is located at Muelle Fiscal, at the town pier, and costs 140 pesos one way to Playa del Carmen.   The ferry schedules can be viewed at the websites of the two ferry companies, Mexico Waterjets at  http://www.mexicowaterjets.com/eng/ or Ultramar at http://www.granpuerto.com.mx/.