To get out of Placencia, just go to the main street and catch the bus at either 5:45am, 7am or 12:45pm. To get to Cockscomb Basin from Placencia it will cost $2.50usd ($5BZE) and it takes just under two hours.
This same bus will take you all the way to Belize city and anywhere in between, if your destination is farther north.
To arrive at Cockscomb Basin you tell the driver you’ll be going to Maya Center. Once you arrive at Maya Center there is a 6 mile road to the park visitor center, campgrounds and trail heads.
There are two options here — a $20-25usd taxi or walking with a bit of luck. The walk is long and a bit hilly, challenging with luggage. But you can sometimes get lucky and catch a ride with a car or tour bus heading your direction. For the best odds, you should plan on arriving in the morning when people/groups are arriving rather than afternoon when most people will be leaving the park.
To exit, buses run past Maya Center about every hour. You can hang around the visitor center anytime before 4:30 and try to catch a ride out. The park closes at 4:30 and there are generally employees leaving in a truck at that time — a good bet on hopping in the bed and getting to the bus stop in time for the 5pm bus. The end destinations to choose from are either Belize City to the north or Placencia to the south.